When I was a kid, our family border collie escaped from the yard. We got home from an event in the dark that night. I didn't see her, but apparently, she had gotten into a porcupine and also hit by a car before dragging herself back to our yard.
My dad, being the perennial cheapskate he is, decided to take her out and shoot her so that we didn't have to pay for an after-hours, emergency vet appointment. She flinched at the last second (or maybe my dad did) and the 20 gauge shotgun blast just wounded her. To make matters worse, the gun broke or jammed or something and he couldn't fire a second shot. He had to call a friend to bring him a working gun. The dog, of course, had to wait the entire time, and I did not find out about how it all went down until years later.
I'd like to avoid something like that. All involved suffered for that decision. Also, I couldn't splatter my dog's brains all over the ground, even if it did die instantly. But that one didn't, and it had to live the last 45 minutes of its life with part of its face blown off and whatever else it feels like to have a 20 gauge discharge inches from your head.
Oh, you'd [insert 20/20 hindsight here]? Murphy's law will strike you too. I'm sure my dad DID NOT anticipate either wounding the dog on the first shot or the subsequent gun malfunction. There's a lot of other things that could go wrong. It just doesn't seem like a very nice thing to do to an animal that will love you like a dog will.
It's funny to watch people try and argue in favor of shooting their own dog, though. The "old ways" die hard. I remember when I got into training bird dogs. The old timers told me that I'd ruin my dog's nose if I kept it inside. That was their excuse for not allowing their dogs inside, you see. 100% b.s., and I ran my dogs in the field against theirs many times after that with no ill effect.