For me it started as an accident. I started reading fanfics only about 3 years ago, after years of thinking all fanfic is badly written and not worth my time. Then I for a reason I can't even remember (I wish I did), I started reading certain TV show fanfics. Thankfully the first ones I read, were so amazing, I was hooked for weeks straight. At the time I was still sure I would never write any myself. I didn't think I could do it. Writing original stories was easy enough, but writing someone else's characters..? No way. Then for some reason I wrote the first chapter for my still ongoing (it's long, that's why) story and left the country for a week. I came back and things have only grown bigger ever since then and I just couldn't stop.
Why I keep writing it now? I've realized that it improves my writing. I keep getting better and better and it's amazing to realize that. Plus, it builds my character and I'm more able to receive negative reviews. Both the good kind and those that are just plain stupid. And with my painfully overactive and creative mind, this is a good way to release some of that constant pressure from my head... It's a win win situation for everyone.
I've even found some good fellow fanfic authors I love talking to and sharing things with each other. I'd never have become friends with them if I hadn't started writing fanfics...
So even if I one day stop writing fanfics, it will always hold a special place in my heart.