Anarchist philosophy is fascinating stuff. From what I can tell, the way you become an anarchist is if the most important thing to you is your autonomy/free will. Naturally, if "the freedom, as a rational human being, to do what I want" is the most important value to you, being in any kind of society where others have authority over you is terrible. And, the logical solution is to form a society of like-minded rational stable people where nobody has any authority over anyone else.
Buuuut, that assumes that everyone in this society would make good decisions and would be rational. What do you do in an anarchist society when someone wants to kill people? Anarchy would work fine in a situation where there is no conflict, but the second there's conflict, there's no built-in system to stop it once it starts.
But if anyone's interested on a nice short "manifesto" of sorts about anarchy that explains where these people are coming from in more detail than I've given, borrow from the library or buy: <A HREF='http://www.amazon.com/exec/obidos/tg/detail/-/0520215737/qid=1089431556/sr=1-5/ref=sr_1_5/104-9200375-5052740?v=glance&s=books'> In Defense of Anarchism </A> by Robert Paul Wolff.
Wow, can you tell I'm a philosophy major? I'm soundin' like Digit over here!
.......not that that's a bad thing, of course!