There are many reasons why people start writing fanfiction. Most of the time, it's because they want to see this one, very specific scenario, but there's no content quite like it, so they're left with no choice but to open a Google Doc and do it themselves.
But other times, it's the opposite. There are fics about the very scenario you want to see, only you find that it either doesn't do the characters and/or their dynamic justice, or it's too OOC, or something like that. So you're left like, "Thanks for the food. Now, let's show these bitches how it's done."