Well, you should read this:http://theanarchistlibrary.org/library/scott-of-the-insurgency-culture-collective-the-anarchist-response-to-crime
You're definitely not going to be convinced, but understanding the point of view is important. This is kind of brief.
Anarcho-capitalism is a different beast though, it's more individualistic. Some ancaps arrive at the conclusion that the state has to be abolished because of its monopoly of violence. Some arrive there for pragmatic reasons. It's also called voluntarism because the thought is a Utopian one where everything is voluntary and there's no coercion. Ancap practical theory is based on the thought that it's economically unsustainable for private institutions to be in war and that there are DRO's or private arbiters as a private court system, etc.
It's complicated, I need to read up more on it myself. Probably need to read a few books too, like this one
To be honest, I'm not convinced myself. I'm bordering between an ancap and a minarchist.. Ethically I'm 100% behind the idea, but I have a hard time letting go of the consequentialist thoughts.