We are certainly not their prey and without modern urban sprawl forcing animals into urbanized areas they would avoid humans as much as possible and this has been true for thousands of years.

Humans are the ones wielding fire after all.

The bears and coyotes around here hide from me! Even if I try and creep on 'em, they still usually sense me and run.

Most animals know humans are too much trouble to mess with.

Sure, you can kill one human. But next thing you know your whole species has gone extinct, or worse, has been domesticated into pocket yappy dogs that can't breathe properly.

In places where we've been around long enough staying away from humans has practically been bred into every surviving predator's instincts by now (which is what makes polar bears so terrifying, they're about the only dangerous predator that doesn't have this instinct yet, and probably never will, now that murdering whole species has become a bit of a bad look); anything that considered us prey and didn't learn not to simply doesn't exist anymore.

Wolves in particular (in the few places where they survive) definitely know not to mess with us, except maybe in the frozen depths of Canada, and so do most bears (again, with possible exceptions in the least populated bits of North America) except polar ones.

Bears usually avoid humans, unless very hungry, because those who didn't avoid us, didn't tend to live very long.

Large predators have a species memory that tells them in general messing with a human scent can easily lead to a bad day for you. Because we have spent millennia hunting and killing them. So they have learned to avoid us directly.

This does not mean that that in certain instances, such as starvation or if they feel cornered and trapped, that you can't get hurt by them. So when I go out into the forest, and where I live we have black bears, wolves, and now permanent cougars-- and not the ones you might find in a bar on Friday nights either --the only one of those three I find a bit dicey to be around is the cougars. Bears and wolves really don't like people and make themselves very scarce very fast once they know you are there if there is an open escape route they can take.

Big cats, on the other hand don't appear to be the brightest bulbs in the box. And tend to be more of an issue for humans mucking about in the wilds where the cats are found. When I do venture out into areas that I have seen sign or even worse, spotted a cat, I do tend to carry a pistol for self defense in those areas. I've not needed to use it and very much hope not to ever need it. But being 'forearmed is to to be forewarned' so to speak.