I'm on the opposite side of the spectrum I suppose. I always wanted to have fur and a tail, or maybe wings. When I was younger I was a huge fan of Gatomon from Digimon, and some point crossed her character with the Pokemon Meowth's evolved form, Persian. I guess I added the wings at some point, possible from Gatomon's digivolved form, or maybe I saw a bit of Cardcaptor Sakura, and based the whole thing off of Spinel Sun. Occult Gakuin was not a thing yet, but most of my imaginings about it are oddly similar to that one scene from Episode 12.
Any psychoanalyst could have a field day with that. Obviously I really wanted freedom, hence the wings. I could only turn into this creature at night, again on this idea that the night was the only time that was truly mine. Most of the books I loved and still love from that time period had this conceit that cats were inherently well-versed and well-traveled in the mystical world, but also aloof. Sandman, Old Kingdom, Alice in Wonderland, Wizard of Earthsea, Discworld, Harry Potter, Redwall. I was obsessed with Egyptian mythology, especially Bast. I loved the idea that a cat knew everything that was happening, but was above all of it. Moving in and out of the protagonist's story line, they treated the protagonist like a mouse, fun to play games with.They were never the central part of the story themselves.
My companion was always a young female human. But I have to state firmly that this was nothing sexual, on the surface at least. I myself had no binary gender, and was also a completely different species, and indeed, a completely different type of living thing altogether. All my real life friends were female then, and now, so I think this speaks towards me wanting a human connection than anything else.
So all that to say this. When I first discovered that people thought all furries were sexual deviants, I was appalled. I was even more appalled when I discovered that most of us are. I might not even be a furry. I just know that I spend a lot of time thinking about being a giant panther with wings. And thinking about it is never arousing in any way.