Because it *is* play, play and not work. Because it's a response to the experience of reading or watching another fictional creation. Because writing a story based in an existing fictional universe is one way of processing the meaning you found there. Because the processes of imitation, derivation, borrowing, and transformation are universal to all the arts, yet we behave as if writers work in splendid isolation. Because it can be practice for writing original work. Because it can be a hobby, like knitting or bellydancing or singing in a choir. Because it's fun.

Sorry, Tony, but after writing fanfic as well as original fic for over ten years now, I'm really getting tired of hearing that question.