Whiiiile I'm thinking about it...
It is very rare that an animal dies of natural causes in the wild. Humans are, really, one of the few earthly life-forms that die of old age; others I can think of off the top of my head would be certain kinds of trees, whales, and maybe sharks.
In the wild, if you get sick with disease, you may die of it, or you may be eaten alive when you can't walk or stand. If you are getting old, that means you're getting slow, and you may die of old age, but the probability is you'll be driven out of the pack/herd/bevy and picked off, or eaten alive when you can't walk or stand. If you're young and spry, like a deer, and you get into snow that's too deep for your hooves and thin legs to get you out of, you'll die of freezing to death, being smothered by snow drifts, or eaten alive because you can't move.
If you, as a human, are old and living in the woods (even if you're young, in fact) off the land, as humans and our subspecies have done for millions (if not billions of years), when you can't run, or are injured, or just careless one day, that bear or wolf you've grown up around, watched since it was a pup or cub, it will eat you. It will put you out of your misery, hopefully fast, but possibly not.
Someone I know raises horses. She raises them until they start to get arthritis and can no longer be ridden or pack goods, or be healthy lawn ornaments and she puts them down and puts them in the freezer, before they are in so much pain they can hardly move and look at you with dying, sad eyes when you dope them up sympathetically with drugs. She believes its more justice to the animal to have a swift death that's quick and to be used, than spending a few weeks or several days or months fading away, withering to nothing.
I can't say I could do what she does. But I get it, boy do I ever get it. How many people have lost pets due to old age? My old dog was arthritic for years before she was put to sleep. She had days where she didn't want to get up to even go to the bathroom, days when getting off the couch was filled with wimpers, but those days weren't as plentiful as the days without the pain. Those of us who have watched that have all thought, possibly years before the day came, is this the time? Is their quality of life beyond what's acceptable?
I think, deep down, putting an animal to sleep, is a predatory instinct, dosed with empathy and an understanding of sentience.
Am I diverting from the topic?