Vortex: I would love to have a fursuit, but I lack the funds to purchase one, and the skill to make one.
Brick: An interesting question, and an unusual one, as most people would rather ask how than why as it is easier. I shall try to answer anyway.
I have for decades been interested in any media with anthropomorphic animals. As I grew older, I came to find a community based around the same interest. I'd say that would be how I became a furry.
I found myself more comfortable with identifying as a furry than other fandom tags, so that would be why I chose to identify as one.