While I have nothing against fan-fiction at all, I tend not to read it, as I usually believe the author knows what is meant to happen in their own book, better than I do, so I shouldn’t try to re-write it just because I don’t agree with whatever happened.
However, writing fan-fiction can be a brilliant way of getting you writing about anything, and therefore writing something.
Anti fan-fiction probably isn’t the right name for it, Fictional fan-fiction might be better, but anyway, if I am failing to write anything, it’s a good place to start.
Rather than just writing about my version of events for a story, I will put in one of my characters into the story to see what they would do in the situation. If, for example, I had a character terrified of the dark, what would happen if they were in the library with Vashta Nerada from that episode of Doctor Who. Or if my character was obsessed with Harry Potter, what happens if they find out Hogwarts is real?
While, it’s usually impossible to incorporate my anti fan-fiction stories into my actual story, as I’m sure that’s some sort of weird plagiarism thing, it does help you: a) understand your character a little better – and who doesn’t love character development?
And b) It gets you writing something. What you do with it afterwards is entirely up to you. But you wrote something and once you’ve done that, there’s nothing to stop you. So now stop procrastinating by watching Doctor Who and carry on writing!