Why fanfic? It's true that it has some disadvantages. Most obviously, there is no hope of ever getting it published through traditional channels because of the copyright issue (occasional Star Trek fan collections notwithstanding). That doesn't bother me in the slightest, though, because that's not why I write. I have no plans to ever make a living doing this; it's a hobby, and I'm happy with that. Maybe someday I'll be inspired to write some original fiction, and then maybe we'll see, but I'm content with the current situation for now. The other disadvantage that comes to mind is the necessary limitation of your audience to people familiar with the source material. Most of my friends will never read my fiction writing because it wouldn't mean anything to them. (And I'm totally cool with that, by the way. I know a few of you have made the attempt, and I appreciate the thought a great deal! But I understand that someone who has never played the games isn't going to get much out of my work.)
But fanfic has one clear advantage, for me anyway, and in the end that's why I write it: the world of Spira gave me a springboard from which to start writing again. For the last several years, whenever I thought about writing fiction, the thought of having to create characters and come up with things for them to do paralyzed me. I'd write a few paragraphs or a vignette and then stop, with no idea of where to take it. Spira and the characters that populate it gave me a springboard, a place to start. Now my creative muscles are being exercised in ways they haven't been used in years. And I think that has spilled over into the rest of my life in good ways. And I'm stretching them in the writing, too; I am creating characters and coming up with things for them to do -- original characters, worked into the fabric of the existing universe. So, that's why fanfic. On some level, I missed being a writer, and fanfiction showed me a way to get back there.
Now, why this particular source. I think that's the bit that T has a harder time understanding. He has played both games, and he in particular has a hard time understanding why I find Final Fantasy X-2 inspiring -- he found the story and the characters shallow, like they were just thrown together to rush the sequel out the door. But the more I consider it, the more I think that's actually the ideal situation for me. All I need from the game is an outline, a starting point. I actually like that, getting to flesh out the details, major ones in some cases, on my own. Really, though, the only answer is that I'm writing about this universe and these characters because they are the ones who happened to grab my imagination. I write these stories because they asked to be written. That may not make any sense to anyone who isn't themselves a writer, but it's the only way I really have to explain it.
So there it is. I don't need to justify it particularly, but I like to think through my reasons every so often anyway. If I'm going to devote so much time and effort to something, I ought to know why.