Do veterinarians always perform the actual euthanasia? Can't they tell their clients : "I'll give you the seringe, I'll show you how to do it, but you will do

Do veterinarians always perform the actual euthanasia? Can't they tell their clients : "I'll give you the seringe, I'll show you how to do it, but you will do it" ? If not, considering that indeed veterinarians probably chose that line of work because they love animals, making them kill animals on a regular basis has to be kind of a death by a thousand cuts.