It certainly denotes a desire by many to not call it "killing", as Commodore pointed out.
It's rooted in the idea that you need to have a reason to kill an animal. I find it hard to believe this would be a novel idea, so just bear with me if this is 1+1=2 condescending, that's not the intent but it seems like it might be a disconnect.
Yes, we kill animals. But if I say "the dog was killed," or "we killed 20 of our cattle today," or "we need to kill that herd of deer," valuable information is missing. Because you haven't provided any justification. You don't just kill things, even if you breed and raise them
to be killed. There has to be a reason. Is it time to harvest the animal for meat/leather/everything else? It's time to slaughter it. The killing has a
reason. Do you need to cull out some unhealthy heifers? Killing them needs a reason. Sometimes you need to "destroy" an animal too. Usage of that word usually indicates less of a "good use" than the other terms. Usually something unfortunate is happening if you are "destroying" animals. It's indicated that this is wasteful, but probably necessary. Referring to the necessity of "destroying" some dangerous animals brings with it the implicit statement that "
this is something we would rather not be doing, it's not a good use of the animal." Does that explain why I get confused when what I think is respectful language is eyed warily and considered being tossed back by people who insist on using, in my eyes,
less respectful language for the situation?