Because answering questions is fun. That's why.
The thing with doing the AMA schtick is that the questions almost always provoke thought. I guess some people might just answer monosyllabically, but I think that's not the point. It's not just a random question someone wants the answer to--it's a prompt. The answer might be simple, but there's always room to expand with interesting anecdotes, pre-emptive answers to possible follow-up questions, elaboration of the reasons behind my answer, and so on.
I could write as if I'm answering a question like "Why do you want people to ask you questions?" and just pretend for my own sake. But that's a lot less fun. For one thing, I have to come up with the pretend question myself, which sort of defeats the purpose, doesn't it? If I already have a topic I want to write about, I don't need to contrive a fake question to answer. And for another thing...actually, that first thing pretty much covers it. It's just better as a two-person game.
I did an AMA on reddit a while back and enjoyed it very much. People asked good questions, and I felt like I had interesting answers to give to them.
I'm a little jealous of Mark Rosewater's neverending supply of inquisitive fans. My inbox is always empty.
But my inbox is also always open, so please, drop something in over at http://troacctid.tumblr.com/ask.