We're not prey animals to them. In natural settings, most big cats will go out of their way to avoid humans. Like snakes, most attacks on humans by them aren't because they're hungry.

It's when this changes that problems start to happen. Big cats looking upon humans as easy to catch meat-on-a-stick (being man eaters) is when the problem starts.

It's unpleasent, but unlike before they now will go out of their way to hunt humans, and it's every species for themselves.