Given that the discovery that alligators can do this is relatively recent, I wouldn't expect there to necessarily be any confident answers, but we can obviously make guesses.

It's apparent why alligators might need to develop some kind of defense against predators. They're born small and vulnerable, and while the adults have no natural predators, the eggs and young have several. Several survival traits are shared between alligators, caimans, and crocodiles, such as large clutch sizes and protection from the parent for the first year or two.

But, a specific adaptation would depend on what the animals chief predators are and a good amount of chance for what mutations happened to occur in the population. Since alligators and crocodiles largely live in different parts of the world, it's conceivable that alligators had predators that were more likely to damage or destroy only the tail, so it was advantageous to be able to regrow it (I don't know enough to speak to what difference in predators they might have).