Aside from the fact that it's a given people who write fan fiction aren't as experienced nor as talented as the people who wrote the actual real, original stories...there are some points which make fan fiction superfluous.
1. The Fan Writer doesn't know ALL that's going on behind the scenes, behind the story told, hence he/she can never know the exact direction where to take the story next.
2. For the same reason, a Fan Writer can never fully understand the characters within the story. This, as you can already guess, makes his character development always at least a bit off.
3. It can, oftentimes, ruin your view of the original works you loved and cherished.
4. The pure existence of thinking that a Fan Writer CAN continue the story, that he, apparently, disagrees with what the author considered to be the ending to his/her work ... is almost always disrespectful.
5. It's never the same! Never as brilliant, never as unpredictable, never as relatable.
Next time, try some real, original work!
You might surprise yourself!