Mother black bears with cubs are primarily interested in defending them. The first thing you ought to do if you surprise a mother bear with cubs is stop, turn around and walk away slowly. Most of the time she will see you are no longer a threat and won’t attack. If she does attack, it is generally only to incapacitate you, to ensure you’re no longer a threat. In this case, fighting back won’t work since mother bears will almost always fight to the death to defend the cubs. In this case, playing dead is your best option, since she will see you’re no longer a threat and will usually leave you be. If you have a gun, of course, you could probably kill her, which would guarantee your survival, but should you? I probably would not; she’s just a mother doing what any good mother would do.
Most do, some don’t. You’re mainly thinking of great whites. Around here (Florida), the most dangerous shark seems to be the bull shark. There are no plump, fatty seals nearby, and bull sharks are very opportunistic. Tiger sharks also seem to be in the same mode.
Alligators will occasionally take people as food, just like they’ll take deer, dogs, and anything else that gets close enough and over which they hold a size advantage.
Well, back in the Pliestocene only a few thousand years ago there were a lot more large predators in North America.
Off the top of my head, you’ve got grizzly bears, short faced bears (Arctodus - Wikipedia), American lions, Smilodon, Homotherium, and other medium-large cats like cougars and jaguars, dire wolves, gray wolves, and humans. Maybe throw in a giant ground sloth, but even if they ate meat occasionally they probably didn’t hunt.
If leopards still today prey on chimpanzees, our closest relatives, (not to mention baboons), then it stands to reason that they once preyed on us, too. To a leopard, hominid = dinner.
Also, primatologists have it as their working assumption that leopards are one of the main predators on primates. Which would include us, since we’re primates. Leopard predation on humans is still an ongoing, and increasing, problem in some districts of India.