Even cops (who are obviously trained on how to kill things) have trouble at times (and yeah, I know they routinely shoot and kill dogs.
The example I witnessed personally, was brought in to the clinic I was working at by the policeman who shot the dog. It was a pretty big pitbull that had apparently rushed out of the yard at the cop when they went to serve a warrant. Dog bit his partner, then turned to him.
I have to give him credit for waiting as long as possible. The dog had powder burns on the nose, and a nice small entry wound under the tongue (i.e. mouth open at time of shooting), and an exit wound under the jaw, and a furrow on it’s chest between the front legs. The guy shot the dog as it was lunging at him with mouth open.
And yeah, totally non-fatal wound, but enough to stop the attack. Cops brought the stunned and bleeding dog to us, we anesthetized and repaired it, and the cop paid the bill. We got instructions to return the dog to the owner’s wife when she came to pick it up.
I was pretty surprised by how the whole thing went down, both medically (the damage was honestly pretty minimal, though a bit shocking looking), and socially.