I’d say depending on how you look at it, that question is either the toughest or the easiest one to answer…
I’d say it’s tough because I’m not sure if I could come up with one simple, specific issue…largely because I would think the hardest thing to even begin to get people to wrap their heads around (let alone be persuaded of) is the abscence of a state period.
In other words, I think the answer is in the question. The toughest thing to persuade people about an-cap, is anarchy itself.
To be perfectly honest, I actually remember not being able to even begin to imagine how a stateless society would work. Literally, I couldn’t imagine it. I’m very glad to be able to remember this mental state. I saw the title of some video online or read something somewhere about an-cap and remember kind of shoving it off as people fooling themselves…kind of like people do with communism. A short while later I came across a series of videos with the theme “in a stateless society” by AntonBately.
I recall seeing those titles and thinking “how the hell would that work?” I recall listening to some of those with great interest, because it was literally an attempt at explanation of something that I literally could not imagine.
Looking back now, and recalling some of the arguments put forth in some of those, from what I remember, they’re not even that good…but it was certainly a start.
Sadly I cannot remember much detail about how exactly my intellectual journey progressed, and what specifically advanced each step, or even what those stepping stones were. But it was definitely a progression. It wasn’t as if I read a single book and was converted. (But then again, I didn’t really start reading the books that might have caused such a conversion until after it had largely occured.) It was more of an incremental thing…a process of simply being exposed to various arguments on various topics as I happened to come across them. I think it was simply a conclusion that manifested as more and more arguments were found to be persuasive…until eventually you kind of realize the overall truth.
So I think a big part of the trick is tackling each issue as it comes up…meaning don’t jump immediately to anarchy every time. Simply guide them to the reality of its unnecessary nature. You don’t have to compromise on principle, and pretend that some government is needed for defense and courts and the like…but you don’t need to start off by saying they aren’t needed either.
You have an advantage in the fact that, because most people can’t begin to imagine a stateless society, they don’t expect anarchy to be a position someone could/would genuinely hold…so they won’t tend to assume such a thing about you. Which means they’ll assume you are at least a minarchist (even if they’ve never heard that term before). This gives you the freedom to lead them to the reality of whatever they’re advocating, without them getting ahead of you and writing you off before you make your case.
For more on this topic see “Argumentation & spreading the word” in The Ultimate Beginner meta-thread. In particular,
To Any Who Were Once Apathetic: What Brought You In?
Why Ron Paul is so effective
Recommendations on policy when dealing with newbs/statists.
Details on best practices