It has occurred to me that such questions are often asked by people wanting to start trouble. The questioner isn't looking for an answer, but for an opportunity to find fault with the answerer. It's like a drunk in a bar asking, "Are you looking at me?" Answer "Yes," and the drunk will respond, "Why? You think I'm ugly?" Answer "No," and the drunk will respond, "Why not? You think I'm ugly?" At that point in the exchange, the only logical course of action is to kick the son of a bitch in the balls and run for the door.

Therefore, I propose that such unanswerable questions be known as "Shit Starters".