It’s not quite that bad. My brother was a veterinarian and in his case, it was very much a vocation thing: he knew he wanted to be a veterinarian by the time he was maybe 10 or 11 and took a remarkably direct route there. The vast majority of the work was fairly routine care, and he had a unique gift for connecting with animals (most of his early career he did house call veterinary work and so many clients would talk about how their cat or dog was terrified of strangers but would just climb into his lap and let him do whatever he needed to do to care for the animal, whether it was trimming nails, examining teeth, taking blood or anything else). Euthanasia was something that he felt, but was able to get through for the other aspects of the job.
I have an ex who became a vet (kind of a surprise in that when we were dating she was an artist) and she has a house call practice with a lot of her work being euthanasia. I don’t know how she can manage that emotionally, but I’d like to believe she’s not a psycho even if she was the one who ended the relationship.