To me, being a furry is associated with a number of social connections. The most obvious one of course is the fact that I'm part of this extended community of like-minded groups and individuals. Also, I'm connected to my animal counterparts. There are rabbits all over the place in my area in rural Northern California, which is probably why rabbits are a popular fursona for local furries. I see rabbits almost every time I'm out. Since I was little, I've associated them with freedom and nature. With that fond familiarity, it's no wonder I developed overtime as a rabbit furry. In being a furry, not only am I connected to other furries, but it makes me feel more connected to animals and nature. In a way, I feel like a more complete human individual due to my identity with an animal.
Of course, on a less serious note, the community, art, and lifestyle are just so much fun, so I'd have an interest even if it didn't come so naturally.