I actually didn't go vegetarian/vegan on purpose. That being said, I'm a HUGE junk-foodie and over-eater so my health is not that great as a result.
It started off with being grossed out by dairy products. I have never eaten cheese, because it grosses me out SO much.
I grew up drinking a glass of milk each meal, and then one day (likely due to my migraine issues) the milk smelled absolutely disgusting. After that, I never drank milk again because the memory of the smell would make me nauseous, even if it was something yummy like chocolate milk.
I didn't have red meat until I was 15. Naturally, I had a very violent reaction and avoided it ever since.
As for any other meat, even if it was something I had always liked, they slowly began tasting and smelling bad to me. This was during a period where I had meningitus and an extremely long migraine, so I imagine that's why.
Don't get me wrong, I can still be around meat and stuff, but I can't eat it without getting grossed out! It's not just animal products either, but that's how I ended up transitioning
As for animals, my dogs are all on a raw (meat) diet. I have no issues handling raw meat, organs, feet, etc for them.