There's no requirement of ethics, morals, or lifestyle in order to be a vegetarian. You can be vegetarian becaise you don't like meat, you hate eating it. you're allergic to it, you want good health, or it's expensive etc.
Vegetarians aren't really trying to save all animals' lives. Not one of them says that. Even the ones who don't eat meat because they don't like the idea of an animal slaughter to attain that piece of meat, they've still not beleiving they're saving all animals. Just supporting a cause.
But there's no actual ethical or moral requirement for the reason to be vegetarian.
If you're a vet, you do have to at least like animals I guess, or be interested in their welfare. But I suppose that's the ones who get injured and are family pets, or a slave in somebody's factory. Either way, they're needed alive at this point.
Some people love their dog then can separate between the dog and a sheep they slaughter.
That is skewed IMHO. BUt never underestimate the power of denial. If something is status quo- then the population loves to believe it's OK.
PS Common Sense Says..people who love animals are not necessarily vegan. I don't really like animals, let alone love them. But I don't use them as slaves because they're living creatures with a right to their own lives and I cannot stand slave owners treating them badly. Doesn't mean I love them.