As a writer and an occasionally disgruntled fan, I can see the appeal of fanfiction sometimes. Sometimes there is just a brilliant idea that isn't treated well, or a great story that just has the least satisfying ending of all possible endings. Sometimes a hint of something is presented and one expects it to turn into a plot element, but it's just ignored. All of these things are frustrating and reasons for turning to fanfiction.
I know there's a lot of people out there who dislike fanfiction. I myself used to scoff at the very idea. I mean, why fanfiction? The story was finished when the author was done with it, right?
Here's where I start to run into some contradictions even within my own mind. I mean, the author decided how the story should go, yes? I know with my works I would take issue with someone going in and mucking them up with their poor grammar and strange shipping ideas, but at the same time, I have read some stories and watched some movies that just beg to be expanded upon. I myself have written a few short fanfics (mostly self indulgent) as I try to read deeper meaning into a relationship or happenstance that seems to be too skimmed over in the original work.
I justify myself with an idea gleaned mostly from Inkheart, and other such works that imagine the creation of a work as the creation of a whole world and even if you don't focus on the entire world in your original story, it still goes on and all the little minor characters have their own stories and interests. The news quote at the bottom of this strip of The Zombie Hunters sort of helps articulate my position. Jenny's just showing a different side of a character there, but what if the story were to focus on another side of the character or another character entirely from those found in the original work?
It's the basis for a lot of retellings of fairy tales. What are those but fanfic works? Alternate origin stories for comic book characters and expanded universe novels for such things as Star Trek and Star Wars? Basically canonized fanfic.
Now, granted, there are a lot of horrible stories out there. I mean, really really awful. It's there that fanfic gets its bad name. Between out-of-character-interpretations and Mary-Sue inserts, there are some really bad stories out there. But it's really no different from original writing in that way. It's just that fanfiction gets slammed for it moreso in the public eye because it's based off of someone else's work and thus can be poked fun at because it fails to live up to the original.
In which case I'm like "Canon is sacred! Zomg! What is your problem?" I mean, I don't like it when fanfics start to get screwy. I prefer stories that either expand on the original (whether prequels, sequels or just interstory expansion) rather than alternate continuity fics (unless, of course, the continuity does not play out the way I want). It's pretty much a subjective things, methinks.
I guess that's what all fanfic is: subjective.