I write fan fiction occasionally, not for Buffy/Angel though. Not because I wouldn't want to or have nothing to say but firstly, because I didn't have a story/idea pop up in my head that practically yelled "BUFFY!" and secondly, because I only recently started writing in English a short while ago, the rest I've written is in German and you do not want to write Buffy or Angel in German. You can trust me on that. So, I don't know if my opinion is legit but it's still fan fiction, so I'll just tell you.
I used to start writing my first fan fic when I was about 12, 13 and, of course, they were atrocious. When I look at those I'm glad I didn't have internet back then yet. But I had fun writing those, I was inspired to write and I think it helped me learn how to write, to formulate my thoughts and put them on a piece of paper/my computer screen in coherent sentences. Those were about a band I liked then and since I had no clue what those people were like in real life and didn't know how to look for character traits, mannerisms and the like yet, I could shape them like I wanted them to be.
Fortunately, I grew out of that and when I started to learn what book, comic, TV and film fandoms were like, I learned how to write a character's personality and keep them in character with what is shown in the source material and how to read between the lines, because it is really hard to keep a character consistent and not make them appear out of character. I learned how to do character studies and, to this day, this is still how I start to shape a character.
So, I think I still haven't explained why exactly I write fan fiction. The reason why I write fan fic is - it came to me naturally, I've always been a storyteller - even before I could write I made up these elaborate worlds and stories in my head and when I tried to tell them to my parents and friends it came out as just gibberish because I had thought of so much and didn't know how to tell them - and I simply didn't have the persistence to put all of what I thought about on paper and, most importantly, it helped me learn. It still does.
I don't think I knew how to write a coherent story or a character if it wasn't for fan fic. On some days, it is just easier to take another person's universe, their characters and then shape the story in my head around it than have to think about everything myself - because setting rules for your universe and then keep within them and bound them just that little bit and thinking about every minor detail is really hard. It helps me relax before I have to get back to the "real" writing, and, if I'm lucky, may be some idea that I can put into my original fiction.
Kelsey agrees: Same here! I was completely terrible when I started, and I learned so much from writing fanfiction. How to be coherent and keep characters in character--everything you said.
Everyone starts out bad and, in the best case scenario, you learn from that. A lot. And that's a good thing. I'm just glad my first few fics never saw the light of the internet because wow, there would have been flaming.
Some published authors - and I'm not naming names, but there's a few - practically discourage their fans to write fan fiction - not for the obvious "that is MY sandbox and I'm the only one allowed to play in it" - but because they say it's lazy and that you should write your own stuff. And I simply don't GET that.
But I don't think you can start with inventing an entire universe and characters from scratch and then keep everything in order. That's hard work because there's so much you have to remember and look out for. It's easier to have something that already exists in some form and have reference on speech patterns, mannerisms, behaviour, etc. Now to keep those within the laws of that universe is hard too but at least you don't have to start from scratch.