Hmm... let me think about that...
Well, when I was about 5, I got a Gameboy Advance for Christmas, and Super Mario Bros. 3 to play with it. I hope I don't need to explain this, but Mario 3 has this power up that gives you raccoon ears and a tail, as well as the famous Tanooki Suit. To me, that game was like magic, and I think that's where my furriness started.
Another game that was a big part of my childhood was Drawn to Life, which had fox-like people called Raposa. I still hold that game high in regard.
I used to have a cat, and my remember my whole life wishing I could be a cat too. I think a bit of my personality is cat-like because of that.
I also used to watch a lot of cartoons, and you know how that works in relation to furriness.
Certainly would explain why I like foxes, cats, and tanukis so much.