There are a lot of people out there who dislike fanfiction- for some of them it goes way beyond dislike and into hate, but that's true of anything which is heavily debated. I even understand their reasoning. When characters live in your head, there's always the feel that they're yours, like some part of you that it feels wrong for somebody else to control the actions of- and that includes settings and worlds, because the setting is as much of a character as the actual characters, as any worldbuilder can tell you. In a way, it is stealing to use something which, as many writers will tell you, is like a part of their soul, even if the original character remains where she started out. It's cheating to take these premade characters and world and just use them, without creating them from scratch or basing them off of people and places you know.
But, honestly, if that's how you really feel about it, don't watch any movie sequels, or watch any episodes of TV not written by the original creator, or movies based on books, or read non-independent comics, because what do you think they are? Yes, they're firmly in the "legally allowed" category, but they hit all of the points that are usually made by people who are anti-fanfiction except for the "it takes money away from the creator" argument- which I have never seen evidence of (and in my experience, getting more involved in a fandom- such as by writing and reading fanfiction- makes me more likely to spend money to buy things related to that fandom).
I've occasionally seen people argue that fanfiction is all badly written. This argument holds at least some water- if you go to the wrong places first, your first impression of fanfiction will be awful: mangled grammar, spelling so awful you know it wasn't even run through a spell checker, and a plotline which both proceeds too quickly and makes no sense, while the only familiar thing about the characters is their names (and sometimes not even that, if they're arbitrarily given nicknames or aliases, or spelled differently each time). We've all seen fics like these unless we stick firmly to the rec lists. The thing is, that's to be expected. It's the internet; if you've been on it for any length of time you know that it's full of people who can't make themselves understood in the written word and delude themselves into thinking they can. It happens in real life, too; the only place it isn't expected is in professional media, and that's mostly selection bias. If you write something and want to publish it on the internet, there's nothing stopping you from doing it unless you a) don't have access to a computer or the internet and can't get them, or b) are under 13 years old and refuse to lie about it. There are probably ways to circumvent those conditions, too: mail a letter and have somebody else and have them post it. Have your mom or your over-13 friend post it. Professional media, on the other hand, have to pay significant amounts of money to provide the media to their audience- printing costs, production costs, salaries, advertisement costs…the list goes on. So they don't take a chance on anything they think might be a flop; as it is, most of the books out there are read 'em and forget 'em books, and most movies you watch once and promptly stop caring about without even telling others to watch them.
Most fanfiction is like that, too- middle of the road, enjoyable while you read it but nothing spectacular. It's relatively easy to learn how to write well, to not break the rules or, if you do break them, to break the right ones. However, it doesn't seem to be possible to teach how to write spectacularly: most of the writing advice I've seen is lists of "don't do that"s, but good writing doesn't have anything wrong with it to be pointed out as not working. Writing spectacularly is more doing things right than not doing things wrong, and that can't be taught. And it's not like professional fiction has a greater percentage which has been awesomely written- out of 16 years of reading everything I could get my hands on, ultimately I can count the books I couldn't live without on one hand, with fingers left over. Since September of 2008 (6 months) I've read 1,180 fics and put 11 of them on the "can't live without" list, which is a better percentage than I have with professional fiction.
As a corollary to the "badly written" argument, there's the ever-popular "it's all smut" argument. And, yeah, there is a lot of smut, but where isn't there a lot of smut? There are even romantic subplots in some action movies. There are major romantic plots in Disney movies. If you don't want romantic plots, move to a convent or something, because they're everywhere. Fanfiction has a lot more R and NC-17 stories, or their equivalent in non-MPAA ratings, simply because there's nobody telling the writers that they can't include them. A lot of fanfiction writers and readers start out reading romance novels (the other major section they come from is science fiction/fantasy, which is a strange combination if you don't take into consideration that those two genres are treated much the same way by readers of mainstream fanfiction as is fanfiction), so they want a strong romantic plot which leads to more than a kiss. And in some fandoms it's hard to find any fic which doesn't have any romance or sex in it, but most fandoms strongly favor headers which tell you things like title, fandom, summary, warnings, ratings, and pairing. I have yet to see a book that does you that courtesy; the back cover might read like a gen story about a caribou psychologist or something, and then halfway through turn into a story about him falling in love with the mountie who rescued him from a bear, and if you wanted to keep reading about caribou psychology and can't stand romance you're out of luck. My personal ratio is skewed heavily towards reading gen, even though most of the fandoms I read are fairly slash-heavy.
I like the "stealing characters and settings" argument best of all of them, but a lot of what I read isn't just blindly grabbing the characters and/or settings and running with it. I've seen some amazing worldbuilding done for fanfiction- things that would have had no place in the original media, whether because of an emphasis on minor or unshown characters, or because they're counter to the overall theme of the piece, or because of length limitations. Stargate SG-1 wouldn't have an episode about their librarian doing completely ordinary librarian things. The Chronicles of Narnia couldn't have Edmund being Narnia's spymaster. Highlander couldn't show what will happen in the distant future. If they live for long enough, TV series can show an alternate reality or two, but they can't show what happens after- or before- that for the alternate reality. They can't show what happens to every minor character. They can't have things which break the status quo too much- even in the middle of terrible wars, most of the good guys will stay alive and named characters won't die in groups; the main love interests will rarely get married; when major things happen, it's always in a way that the characters are able to get involved. And people read media differently- not only does it have themes and symbolism the creator might or might not have been thinking about, but two people can read or watch the same thing and see it differently; for any given instance two people can take it in and between them believe three different and mutually exclusive readings of it, but you don't necessarily know what anybody else is thinking about it because everybody thinks differently. Fanfiction sometimes shows those differences in thought, and readings of the material that obviously aren't true, but would be interesting (or heartbreaking, or disturbing) if they were. Occasionally, fanfiction reads as more canon than canon, and you wonder how it can possibly not be.
So really, I can understand why some people don't like fanfiction, but if you're not the creator of either the original or the fanfiction, why rain on everybody else's parade? It doesn't involve you, and most people do respect your wishes to not distribute fanfiction if you are the creator.
