(Then again, I recently answered the creepy questions for a friend of mine, so it's not protection against someone you know stealing your identity.)
I don't know why Airbnb needs to know your identity, but I could come up with some reasons. Imagine someone signs up under your name as a host, and their first guests have their laptops stolen. Your name is going to appear on that police report, and that's a pain for you. If the whole fake identity scam can be nipped in the bud, though, this won't happen as often, making life easier for more than just Airbnb's users. I don't think that's a terrible thing.
In a business where you're having total strangers stay in your house, is it really an invasion of privacy to ask you to verify you are who you say you are? This isn't an online blogging service or something, after all.