I was raised in a typical conservative, catholic household and taught all the crap that normally goes with those two. During the Obama period (I was a young teen) I began to fantasize consistently about revolution. It was mostly about abortion - being conservative and catholic, I was naturally pro-life, and didn't realize how non-obvious that issue is, so I thought it was definitely mass murder and that no decent person would disagree. When I saw Obama get reelected, I decided that for sure we needed a revolution to reestablish a minarchist, pro-life, constitutional democracy.
My memory of how I converted to anarchism is a little fishy, but here's my attempt at reconstructing the full story.
It was happening around the same time as I admitted to myself that I had left the catholic church, though I still lied to my family about that out of fear. I frequented Catholic Answers Forums and actually ended up using two accounts: one that I posted on by day where I pretended to be catholic but otherwise had my authentic ideas, and one where I was honest, which I would sign into at night when no one else would walk in the room and see me.
I ended up reading a thread by a catholic anarcho-capitalist and while he didn't make his points very well and I was coming from basically the worst place to be persuaded by his angle, I took the position for a brief moment that "government just exaggerates culture, it makes a bad society worse but a good society better". I wasn't even taking the Ancap's side and still the statists strawmanned the crap out of me.
So that experience led me toward thinking harder about the philosophy of the rebels against Obama I always fantasized about and how they resolved earnest disagreements about strategy and stuff. One day, I said to myself: "As is self-evident, everyone should do what they think is right. If individual agents disagree on the best way of fighting evil, they should try as hard as they can to convince each other, but if they can't, then let conflict ensue". That was the only possible answer since obviously it could never be right to do something you thought was wrong.
And I extended this to all human interaction and didn't ask myself how the principle interacted with property rights. But I could see now that statism was evil because the state doesn't try to convince you their way is better, only threaten you, and doesn't respect that you're an earnest moral agent too and that from your perspective you have as much right and duty (this is really how I put it at the time) to force them to do what you believe is better as they do from their perspective. They treat you like an enemy for disagreeing with them about the best way to promote justice instead of a misguided ally. And that's not even to mention that government actors got their laws from votes instead of doing what they believed in.
I labeled my philosophy "Chaos Anarchism" for quite some time. I embraced the notion that there'd be more conflict in my ideal society than in this one. I considered day-to-day conflict between earnest people a sign of devotion to one's beliefs. A core thing I said was, "it's better to have a world where people fight and die for their beliefs than a world where people submit to rules they think are unrighteous". Hence the name.
And I even still completely stand by that argument. But it wasn't until I started reading some other An-Cap philosophers like the writers at liberty.me that, while I disagreed with their NAP absolutism, I realized that I was selling Anarchism way short. Anarchy is more moral and way less violent and more efficient.
The crucial thing I was missing was the value of consent. Ever since I became a philosopher I've been trying hard to formalize a complete moral code, and for most of this journey I was on a model with "eight cardinal virtues with four subvirtues each". But I hadn't codified the value of consent anywhere. My list contained Kindness which meant that causing suffering was morally bad by default, but my system didn't anywhere acknowledge the difference between stealing or forcing someone to make a sacrifice and receiving a voluntarily gift or favor at the giver's expense. Obviously forcing someone is upsetting and thus would be more against Kindness, but the value of consent is beyond that. It matters even if it doesn't cause additional emotional suffering.
Today, I'm on a 5-value moral system that bears little resemblance to the 8-value one. Consent or Peace is now a prime value, and orthogonal to Compassion. So forcing someone to do something is against both values and is twice as evil. (Usually more because of Fairness, and when I add in additional considerations it can easily come out to 3 or 4 times, even if I assume all values are equally weighted). So I've ended up pretty close to Anarcho-Capitalist morals in practice. But I'm not a NAP purist.