I always represented myself with my fursona so I may say I always have been a furry?
But it was only feral at first.
I knew about anthropomorphic characters thanks to popular cartoons like Donald or other things like that, and always loved these kinds of characters a lot. When I was getting these kids magasines with lots of various cartoons, I would often skip the ones with humans, and only read the ones where the characters had animal heads.
I quite randomly discovered furry art on the internet. I really have no memory how I've found that website, but I clearly remember of some board where there were lots of furry pictures (mostly clean, but sometimes some dicks). And I loved them. So much. I started collecting some pretty pictures and looking for anthro roleplays or creating some. But I didn't knew about the furry community. To me, "furry" was just the name for these anthropomorphic animals.
At high school, I met that weird boy. When I first saw him, he looked like a wild dog growling at the humans around. I really was seeing him as a wild dog, without being able to explain why. I always loved dogs, so, of course, I had to try to tame this one :p
So, we became friends. He was a really weird guy, considered an outcast by most of the other students. He talked to me about himself and told me he was inhabited by the soul of a dingo. It was my first contact with a therian. He ended up discovering the therian community, and, thus, the furry community as well. Knowing that I used to represent myself with a cat, and claiming that I am a cat (I am not a therian, I do not believe in souls nor reincarnation, but I was still claiming that I am a cat, but not for therian purposes), he introduced me to the furry fandom. This is how I first met the community. It was nice talking with all of these people who were into furry characters just like me, until I understood what kind of art they actually truly were into, and until they started to tell me about how they were having sex with dogs or this kind of things. So, I quite quickly ran away from the furry community, while my friend started within, until having the community within him (and he actually wasn't even consenting). But that's another story.
It took me years to try to come back to the furry community. Because I loved anthro characters to much to miss a chance to share about them. I've found that, while many furries are mostly into animal pron, there are still lots of people who likes clean art as well (and even if they like porn too (as there is nothing wrong with this), they are able to talk about something else, and don't try to force me into furry porn), so I joined some french furry groups on Facebook, some furry clans on some random forums and websites, and, later, I joined this forum as well.
Because I actually like the furry community beside its yiffy sides. So, I'd say I became a furry the day I accepted to be kinda part of the community ?