As an Anarchist who spends a lot of time in anarcho-capitalist circles, and also some time in anarcho-communist circles trying to win them over, I've gotten fairly tired of having to debunk the same arguments again and again, so I'm going to try compiling an FAQ of sorts where the most common bad talking points raised by both sides are refuted.
"If I'm doing the work, why is my boss getting most of the profit?"¶
If I make toast using your bread and your toaster, am I entitled to the toast? In a typical job, you make use of tools and a facility provided by someone else, analogous to you providing me with bread and a toaster.
If you disagree about the legitimacy of your employer's claim to own the tools and facility, raise that instead. This argument obscures the real disagreement between you and an Ancap by presupposing the principle that everyone's holdings should be proprtional to their effort.
"My boss is obviously not paying me what my work is worth, because if they did, there would be no profit for them."¶
That logic doesn't work because value is relative. If I have a loaf of bread but no water and you have a bottle of water but no bread, I could give you half the bread in exchange for half the water. In this trade, even though we're not changing the amount of stuff we have, both of us profit. That's why you can't argue from "A is making a profit in this exchange with B" to "B is not also making a profit" - there are obvious counterexamples to that reasoning.
"How is it fair that someone can inherit tons of wealth and never have to work a day in their life, but still benefit from others?"¶
If Alice gives a gift to Bob, she is not exploiting anyone.
This does not change if Bob is Alice's son.
This does not change if it happens at the moment of Alice's death.
If this results in Bob never having to work, that doesn't mean he or Alice exploited everyone else unless what you really dispute is the legitimacy of Alice's original property claim, in which case, argue against that instead.
Remember that, see above, benefitting from others does not mean exploiting them.
"My boss shouldn't be able to order me around on the job."¶
Okay, I'm coming to your house to use your computer and you can't control what I do with it.
Again, the real disagreement seems to be about the legitimacy of your boss's property claim. Argue against that instead of a consequence of it, if you want to promote understanding.
"Property requires violence to enforce."¶
Stopping murder requires using violence against those who do it. Ancaps think defending their property is the same thing on a smaller scale, so this argument is circular. Once again, target the legitimacy of property.
"If it's greedy to want to keep everything you have, how is it not greedy to want to take what someone else has?"¶
This is a circular objection that presupposes the Ancap value system. A communist disagrees that people retaining possession of what they naturally acquire is of supreme importance to ethics.
Also note that this can be made to look the opposite way: while a poor socialist appears greedier than a poor capitalist, a rich socialist (let's assume a nonhypocritical one) appears less greedy than a rich capitalist.
"Communism has failed historically"¶
Most Ancoms believe historical communist nations did not practice anything close to their principles, so pointing to the failures of those socities as proof of the failure of anarcho-communism is pointing to the failure of an ideology that your opponent rejects as an argument against your opponent's ideology. There's no shard of logic to it.
But that's No True Scotsman
Not any more than it's No True Scotsman to argue anarcho-capitalism doesn't have the problems of modern American corporatism.
"You can't argue against capitalism while you're benefitting from it"¶
Entirely wrong and hypocritical. You can think a system is corrupt even if you benefit from it. If I steal a hundred dollars from someone else and give them to you, are you going to take "you can't criticize this system of exploitation because you benefit from it!" as a defense?
Besides, the premise that they're benefitting from it is in dispute. This argument is no more valid than when statists say "You can't say the state is illegitimate while you use its services".
"Communism requires a state"¶
Ancoms don't think so. Whether their ideas can actually be successfully implemented without a state is wholly irrelevant to the question of whether they want a state, and outside of that, this is a conclusion that takes arguing for, not a premise to take for granted. Note that Ancoms usually accuse Ancaps of being statist "because private property requires a state to enforce". If you don't want to hear more of that BS argument, you shouldn't raise it against them.