Again: As a writer, I'm opposed to fanfiction.
But I'll let Robin Hobb explain exactly how, and in how many ways, fanfiction is wrong.
I must emphasize Hobb's argument that Fanfiction is NOT a good way for people to learn to be writers:
"Fan fiction is a good way to avoid learning how to be a writer. Fan fiction allows the writer to pretend to be creating a story, while using someone else’s world, characters, and plot. Coloring Barbie’s hair green in a coloring book is not a great act of creativity. Neither is putting lipstick on Ken. Fan fiction does exactly those kinds of things."
-Robin Hobb, "The Fan Fiction Rant"
Speculation: To become an original writer, perhaps first you need to develop a sense of who you are. In other words, you need to learn where "you" is located in the world.
The act of writing, like all personal expression, CAN help you find out "who you are"... but ONLY if you try to explore own experiences, your own memories, your own senses.
To ape other people's writings will NOT do that for you -- in fact, it may trap your mind in a mental cocoon and prevent it from developing further.
But why listen to me, or to Robin Hobb? Listen to the large community of fanfiction fans instead: Fanfic - a force of nature.