Your problem - and it's a problem everyone has with anarchist political ideas - is that you're still thinking in terms of the society we currently live in. Uninformed individuals who, because they are uninformed, cluster together for comfort and security; they look to someone to lead them, instead of making decisions about leading themselves.
Thinking about anarchism has been, for me, similar in how far it's bent my head as when I first started reading about quantum physics, and the comparison isn't that specious either; when you spend X years of your life learning about the Newtonian/Einsteinian universe of predictable events and the idea that the heavens are a giant piece of clockwork, the first time you read about QM your reaction is 'Fuck off, you can't do that! What about causailty!'. The same thing applies to thinking about anarchism - you have to move past your life's programming, from when you were a little kid, that there will always be someone more powerful than you to take decisions and lead; that there will always be a written framework of rules and laws to govern your behaviour - no matter how arbitrarily those rules and laws (even here there's a big difference between the two) are applied. With anarchism all that framework has to be built by you, and everyone around you in you own mind. Rather than be governed by arbitrary powers-that-be, you govern yourself - you are a nation of one, and everyone else around you is the same.
The difference this could make is huge. People would be good - in the Confuscian words, virtue would be seen as a way to be in and of itself, as opposed to simply not being bad, which is how we behave when subject to law (how many people believe that the only time you're guilty of a crime is when you get caught?).
Don't worry if you don't get it - I didn't for years, and TBH it's only in the last few months that I've actually got my head around it geneally (more specifically this morning, as I mention above).