Quite. By the same token, if I took my healthy dog into my vet to have it euthanized, I am sure my vet would refuse to do so, and probably inform the relevant authority.
Actually that happens often enough that it has a name: convenience euthanasia. I believe most vets will try to find alternatives before they go through with it, but some physically healthy animals are definitely put down due to behavioral issues.
Some vets will do it but not most according to my vet and vet tech friends. (Anecdotes, unfortunately.)
They find even the proper application of euthanasia terribly emotionally draining though. It's being confronted by the feelings of the human family that is the worst for them.
