Despite their frustrating nature to many, the fact is that stereotypes almost always have a grain of truth at their center. A stereotype is a generalization, and a generalization would not exist if there wasn't some evidence supporting it. The generalizations about fanfiction is that they're typically unoriginal and poorly-written by pre-teens and teens who can't take criticism and think they're awesome. And while there are many brilliant fanfiction writers out there, the truth is the stereotype has much more evidence than they would like to be taken seriously. There are a lot of very poorly-written and unoriginal fanfics out there.
But the question is, why fanfiction? Why is it that this piece of creative expression in particular finds itself with such a massive portion of rough compared to diamond?
The first is the fact that not everyone takes to writing and creating naturally. Some people do it really well by instinct, creating stories that flow and are interesting, enough that maybe even the occasional cliche and overused concept can pass by without too much comment. Then there are others who struggle with coming up with their own ideas and struggle even more with fitting sentences together so they work well. Some may actually manage to develop their own concepts and get going on them, but suffer from many of the mistakes of amatuer writers, such as awkward syntax, spelling and grammatical errors, cliched plots and poor characterization, among other things. These things reign eternal, something that critics of fanfics often forget. Fanfiction alone does not a bad story make.
However, it does have this downside. Many times, fanfiction can be seen as an "out" to those who are struggling with their own ideas. Instead of making up their own universe for their heros and heroines to struggle through, they can use ones created by J.K. Rowling, George Lucas, The Walt Disney Company, C.S. Lewis, or any of the other sources many fanfiction authors use as inspiration for their work. Instead of working at developing their own characters, some - though not all - decide to take and work with the characters they enjoy watching or reading about. The cliches are still there, but because of their setting, the seem amplified. Poor characterization is immediately noticed by other members of the fandom who know the characters as well as the author.
Another problem that plagues fanfiction is when the universe and characters are overly manipulated to suit the author's desires. If a fan is not satisfied with something in their fandom - such as a relationship they disagree with or dislike or a plot twist that they didn't want to happen - many fans will try to write the story the way they wish it to be. Not always is much care or skill taken in such instances. The author of fanfics such as these may be in such a hurry to change what they disapproved of that they forget that there's more to a good story. Others may neglect to notice or care that the idea of a relationship between two canon characters that they're so fond of would be totally against what each character would normally do (thus the phrase "Out of Character" or "OOC"). Thus, the characterization seems poor. There's also the fact that if one fan has thought of this idea that they wish to change, there are likely several thousand who had the same idea. If just a fraction of those all write fanfiction based on the idea, then what's left is a pile of fiction based on one idea, enough to make it seem overdone.
A variation on this theme is the infamous self-insert, where the author puts either themselves or a character representing them into the story. This idea is associated with bad fanfiction in particular because the idea is so incredibly overused and so often misused to give the author the pure limelight or enact some fantasy the author has had, such as relationships with main characters or villians, or being the hero of the story in question. Oftentimes self-insert characters that are subject to their creator's fantasies will also be subject to Mary-Sueism or Gary-Stuism, given people's general inability to judge how they themselves would act realistically in a given situation. Instead, they revert to their ideal reaction, and thus attain the flat "perfection" that makes Mary-Sues and Gary-Stus so looked down upon.
The culmination of all this is that the few genuinely good fanfiction pieces out there are underappreciated and unknown. They are so outnumbered by poor and mediocre pieces that instead they are unfairly labeled and treated with contempt. What with all of the problems plaguing fanfiction, one would think that the truly great and original pieces of fanfiction are an even bigger achievement than if an author did the same with their own story. The guidelines to being great are tougher, and appreciation harder to come by.
The thing that we as artists must applaud is their determination to take their work so seriously, and to do things that they enjoy despite the negative stigma. They are part of a form of self-expression that is subject to such an unfortunate combination of situations that it is hard to shine. But they do it anyway. And after all, isn't the joy of creating what self-expression is all about?