Other topics and potential discussions aside...
Nearly every shot that I have ever chosen
not to take on an animal* was out of respect for
them. I didn't believe, 100%, that the shot would be exactly as lethal and effective as I desired; so I let them walk.
I don't want the animal to be gut-shot and running for its life as its intestines snag on shrubbery; or to run 3 miles (or more) with half of its face missing; or to spend three nights on the mountain with three broken legs and a grenaded knee, because of me. (I've seen it. Dirt-bag 'hunter', cow elk, seventeen bullet holes, three broken legs [two with compound fractures], a grenaded knee, guts hanging out, three days to track it down, and it was still alive and trying to run. Broke my heart.)
If I can't take them cleanly, I will let them live.
They are living beings, and I respect their daily struggle to exist. (I hunt out west. I understand it sometimes isn't quite such a 'struggle' in other parts of the country.)
*(I will admit that there have been a few shots not taken simply because the situation would have meant tremendously more work for me, even though I had confidence in the shot itself. Sometimes, I'd rather be lazy than fill a tag.
)