Most people seem to recognize the government that rules over them as more or less "corrupt", but in fact the whole concept is morally depraved.
The moral illegitimacy of government
First, let me dispel the notion that there's any moral obligation to follow the law. There are four possible ways you can be morally called do what someone else says (besides their commands being things you should've done anyway):
When handling someone else's property. While you might argue things like roads are the government's property (they aren't and we'll get to that), at best that would cover a tiny subset of laws. Most importantly, taxation itself can't be justified on this ground, because the earnings of your labor are your property, not the government's. Furthermore, said government property exists because of taxation, hence why we can't consider it "government property": you can't build something with someone else's money and then claim it's your property.
When in debt. But you don't owe anything to the government. You might argue that they protect you from crime (they don't and we'll get to that) or build roads or whatever other benefits, but they fund all those things with your money, so it's not a favor; at best it's a transaction and there's no sense in which you owe them obedience for it, even if we assume you consented to the "transaction".
Altruism. It's morally admirable to help others when you can do so easily, but this is obviously of no use for justifying government because you don't arrest someone for refusing to act in altruism.
If you gave your word voluntarily. This is the big one - opponents of anarchism often declare that a legitimate government rules with the "consent of the governed". Unfortunately for them, none of us ever consented to this system. We've been forced into it since birth whether we like it or not.
A common response is that a democratic government is okay because the leaders are chosen by the people. The obvious problem with this argument is that it treats "the people" as a single person. In a group of 5 friends, can 4 of them decide that "the group" wants to go out to dinner and force the fifth to come with them? You need unanimous consent for a group arrangement, not just a majority, not even 99%. Likewise, you can't say "the people" chose a leader unless you mean all of them.
People who are determined to defend government will often try to argue that even if a citizen of a democracy doesn't vote for the winning candidate, they somehow consent to be ruled by them anyway. They'll argue that by voting at all you agree to accept the outcome of the system. But of course, many people don't vote, so that argument doesn't cut it. Some defenders of government claim that not voting constitutes consent to be ruled by the winning candidate because you didn't use your vote to express nonconsent. Notice something fishy about this reasoning? It requires all three of:
If you vote for a politician, you consent to be ruled by them.
If you vote against the winning candidate, you consent to be ruled by them anyway by participating in the system.
If you don't vote, you consent to be ruled by the winning candidate by not voting against them.
So according to this argument, any course of action constitutes consent to be governed by the winning candidate. Obviously, this reasoning is bunk. (Not only are they not all true, but they are all false, as we will see later.)
Another common one is "if you don't like it, leave", implying that just living in your house constitutes consent to be ruled by the local government. This is a circular argument because it already assumes the government owns the area they claim to. I couldn't go to your house and say "You have to follow these rules, and if you don't like it, you can leave your house". I can only do that in my house.
Another is the "lineage" defense, another favorite of constitutionalists: that the founders of America consented to the system, and that we're bound by their decision. But no one would ever apply that same logic to anything else. A contract I sign doesn't bind my children, let alone for the rest of their lives!
Besides, even the formation of America wasn't unanimous.
Clearly, there's no basis for a goverment's authority. But they're in desperate need of a basis because they impose it with violence: if you break any of their "laws" or don't give them the money they say you "owe", armed enforcers come to take you away, and will escalate force if you resist. We're now scrambling to find a difference between a government and a Mafia gang who moves in and says, "You all consent, you have to give us half your income and do whatever we decide but we'll let you infleunce who our leader is every few years and build a couple of useful things with the money we steal from you". (Spoiler: there isn't one.)
You might still think it's possible to have a benevolent government if the only laws they enforce are just prohibiting objectively immoral behavior such as murder. Though note that this means it isn't a democracy. If your laws are determined by objective, universal principles, they can't simultaneously be determined by popular vote. Certainly it would be admirable to use all the power at your disposal to stop murder even though you know you don't have authority over anyone. But even if you erase all unjust laws, there's still a massive difference between such a government and a conscientious vigilante: funding.
Governments get their funding nonconsensually through taxes. Do you disagree with some of their actions or their methods or just think they're ineffective and someone else would be a better protector of justice if given the money? Too bad, better pay anyway or you'll be put in jail.
There's no way to come close to morally justifying this. No one would ever a defend a vigilante doing it and saying "it's everyone's duty to fund the enforcement of justice", no matter how effective or how uncontroversial the vigilante was. It's called extortion, and it's insanity.
Practical concerns about anarchy
So that's it for the principle arguments. We've established that governments are no different from crime syndicates who extort massive amounts of their victims' money and restrict their freedom while offering just enough token services to convince people that it's "for their good". Now of course I need to put down several concerns about how a society without government could solve all the problems of building infrastructure and stopping violent criminals.
Obviously, there would still be violent criminals in an anarchy, and they would need to be stopped. This is the most common talking point for people who say "well I don't see a way it could work off the top of my head so obviously anarchy is impossible and we need the violent state to protect us from violent criminals".
There is no reason protection can't be provided as a market service the way most things already are. Even necessities are provided successfully this way: if you want food and can't or don't want to grow it yourself, you buy it from someone who has it I realize there's a concern about welfare here; many poor people in governed countries are sustained by welfare programs. I get to that down below. Therefore, if you want people to protect you or find the person who robbed you, you pay them.
Private security is already a thing, but hasn't been allowed to really compete with state police because you're forced to pay for the state police regardless, meaning there's no competition allowed. Getting rid of the government monopoly on police would have several benefits:
More options. If protection was treated as a market service, there would be many different groups offering protection services, just like there are many different companies offering every other type of good and service. If you think one protection agency is ineffective or you disagree with some of their methods, you can employ a different one, or none of them, or try to go into business as one yourself. You take charge of your own life. With a government, we're all forced to patronize the same provider. And we should all be well familiar with the problems of monopolies.
Incentive to provide better service. Since each firm offering protection services could only stay in business by being voluntarily employed instead of forcefully extracting taxes, they'd have to do their best to make people want to employ them. That means anyone who tries to enforce bizarre laws that nobody wants enforced or use cruel and disproportionate punishments on the criminals they catch would be likely to go out of business even without anyone fighting them. Similarly, they would have to keep their prices low or all their customers would just hire a different firm.
Police, on the other hand, don't face any consequences when a citizen they're supposed to protect is dissatisfied, but the employing government isn't. When the police abuse their power and hurt innocent people, the only mechanism to hold them accountable is through government courts... gee, there are totally not any incentive problems with that.
Incentive to solve disputes peacefully. When two anarchist protection firms disagree on a case, instead of fighting each other over it, they have every incentive to try their hardest to find a peaceful solution. Why? Because violence is expensive! If you go to war with another protection firm, your employees are going to die, and that's assuming they don't just say "No I'd rather not kill and die over this messy situation" and quit working for you on the spot. You'll lose customers too because most people would rather hire someone who's going to try harder to solve disputes peacefully.
Compare this to a government, where the police don't pay the economic costs of their abuses of power; whatever costs they rack up are distributed across the entire country through taxes instead of being centered on the people responsible.
So anarchist, market-based "law enforcement" is really a strict improvement over government police.
Poverty presents a much more interesting objection: if we abolish taxation, we have to find a better way to provide for the economically unfortunate. There are several parts of the answer.
The first thing I always point out here is that government is in large part responsible for poverty. Market regulations that take away poor people's options, a broken coercive school system, prisons, wars and massive government spending programs make us all poorer because we're the ones who have to pay for all that shit. So while it wouldn't solve the problem entirely, getting rid of governments would make us all better off.
It's also important not to discount the large-scale examples of voluntary charity in the real world. Those would all still exist! And they'd be more powerful, and more people would feel fortunate enough to help the poor for free, if we were all richer.
Now, you might think these things have been demonstrated to be inadequate because there are people in America who are literally kept alive by government handouts, and that the difference wouldn't be made up by the increase in general prosperity. But have you considered that _voluntary methods aren't working because involuntary methods are being used?_ If the government's taking my money already and to feed starving people, I'm less likely to feed the starving people myself, because I only have so much money to spare. So we should expect that without taxation and government handouts, voluntary charity would rise to fill the gap.
But this may not be enough. The other major part of the answer is contractual obligation: anarchists can and have formed mutual aid assocations that are essentially a voluntary contractual agreement to provide aid to the least fortunate among them in return for the possibility of them eventually being that least fortunate. What I'm describing is really just like taxation except that people can choose not to participate in these arrangements (and then not be eligible to receive the benefits themselves when they are in need). The number of people who are concerned about abolishing govenrment welfare indicates that many people would participate in them voluntarily.
(There is also a large faction of anarcho-communists, who could tell you some different perspectives on this.)
As far as protection services for the poor in particular (a common objection is that market-based protection services don't work because the poor can't afford them), there's a simple answer: a contingency fee paid with the restitution.
If a criminal hurts a poor person, the poor person wouldn't need to have money left to hire a protection agency to get it back; if I were a protection firm CEO I'd offer to catch the criminal, make them perform restitution, and take the cost of my services out of that and give the remainder to the victim. Especially since justice in an anarchist society would be restorative rather than punitive, we'd favor restitution or penal labor over imprisonment, so the victim and I could both profit of the event.
Another common objection to anarchism is the idea of "public goods". How would we handle road maintenance? (The roads question is, in fact, a meme in anarcho-capitalist circles because of how many times each of them has answered it, and how terribly inadequate it would be as a justification for the state's violence anyway.)
To give my own answer, the roads question depends on who we consider to own the roads at the start of the anarchy's lifetime. Given that the people who built it did so with money stolen from millions of different people, I think they would be shared property. It makes the question very complicated, I admit, when you have to solve it without stealing.
Maintanence projects could use a threshold-pledge system. It might be fair to deny access to a road to someone who freeloads to such an extent that they cause a noticeable increase in costs. Rich investors would have an incentive to pay the brunt of the cost of roads that affect them. For example, if most people's ability to access your business depends on a road, you'll want to keep that road in good repair even without being forced. Newly built roads could be treated as the property of those who built them.
While I know my answers aren't completely satisfactory, having some issues with road maintanence pales in comparison to the evils committed by states, and note that it is not a difficulty with anarchy itself, only with converting a governed society to anarchy. If we didn't start with this awkward shared property situation, roads built by private investors and funded with threshold pledges or toll gates would be a completely satisfactory solution.
It could be argued that the biggest benefit of all of anarchy is that governments are responsible for every war and large-scale atrocity in history. Without political monopolies on power, massive war machines that are only possible because of taxation, and the poison of national identity, there would be no wars anything like what governments commit. Even if an anarchist protection agency was corrupt, they wouldn't kill millions of people and ruin millions more. Economic incentives don't involve such wars because, as I've pointed out, violence is expensive when you aren't a government.
Some people after hearing that argument try to frame it as a bad thing about anarchy: well sometimes you need military might, an anarchist society would be easily conquered by a government.
I find it bizarre that anyone who's ever seen a map can make this argument. Most countries don't have the military might to resist an invasion by a country like the US. And yet they stay sovereign. That's because war requires one more thing: an incentive to invade.
And in fact the incentive for a government to invade an otherwise thriving anarchy is even weaker than the incentive to invade small countries. They would know that even if they won, every citizen in the former anarchy is going to be a criminal, breaking unjust laws at every turn and undermining the state in all sorts of ways. The probability of rebellion, guerilla tactics, assassination of leaders, etc, would be astronomically high. Conquering an anarchist society would be more much trouble than its worth for a government.
Finally, if a foreign government really did wage war on an anarchy, the anarchists would have some advantages:
No civilian disarmament laws. Anarchist civilians would be very likely to be armed and willing to defend their homes from the invader.
No single point of failure. They're not affected by taking out a few important individuals the way a government is.
No misalignment of incentives. On the country's side, the people are being taxed and possibly drafted for a war they don't have a personal stake in, and as soon as popular support falls under 50% (assuming a democracy), the government has to pull out. Whereas the anarchists are defending their homes and very much do have a personal stake in this. All those different protection firms would have every reason to work together to fight the enemy that threatens to put them all out of business.
The biggest advantage of all: First strike. The government's goal isn't to wipe out the anarchy, so they can't just march in and shoot everyone. Presumably their goal is to disarm the anarchists so subjugation becomes possible. But this situation where only one side is unable to shoot someone from the opposing side on sight basically guarantees that the anarchists will have first strike in every confrontation.
One more thing...
There's one last point I want to make. I made a bunch of arguments up there about how an anarchist society would not be a world rife with violence. But more importantly is that it doesn't matter if it would involve a lot of violence. Isn't people getting hurt because they disagree about what's right better than people doing what they believe is wrong? If there was a planet full of conscientious and benevolent but impoverished people and a planet of selfish hedonists living in near-utopia and you had to destroy one, which would you destroy? Would you rather have suffering or evil be rampant?
I'd refer you to more anarchist reading if you're not fully convinced. Besides my other article where I detail many pragmatic downsides of government, Roderick Long has a PDF on Anarchism where he focuses more on the practical concerns. His version is slightly different from mine due to his stricter adherence to the non-aggression principle, but he makes lots of good points. ESR (a renowned open-source contributor) also has some really good articles on why he's an anarchist and the myth of man the killer. Backalley Philosophy is a youtube channel with some amazingly accurate videos on the topic.