Ornery cats can occasionally chase of some pretty large critters. I recall someones blog post where there house cat had treed a grizzly cub.
But it probably is not a great survival strategy. There is a reason that most cats will run and hide, or clime a tree. Because it works more often than not.
But why do the alligators, and baby bears back off? Partly because they are confused. But also because they are instinctively are reluctant to risk injury. Animals don't have access to advanced antibiotics. A bite or scratch has the potential to become fatal. Most animals avoid pitched battles, unless it is from within their own species.