Why is whataboutism so prevalent?

Of course it’s human nature. When Aristotle said that man is a rational animal, he didn’t mean that human beings are perfectly logical. He meant that we have the capacity for reason, and that it is in our nature to use it as one tool among many when navigating our way through life. But reason is a treacherous landscape. A rational animal is still an animal, after all, and fallacious reasoning is common because it both seduces and deceives. It seduces by shepherding us towards what we want to be true, and it deceives by masquerading as a legitimate argument.

Everyone has these tendencies, though not everyone takes the time to battle them. And not everyone who takes up the fight succeeds. This is especially true in the case of tribalism—the motivational instinct behind whataboutism and related failures of reasoning. The best way to combat it is to not conceptualize oneself as being on a side or part of a team, but that runs counter to nearly every social instinct we have. For as much as we are rational animals, we are also social animals. Choosing sides runs deep in our veins. It satisfies a need for belonging.

The Founders knew this. Washington warned us in his Farewell Address that “the alternate domination of one faction over another, sharpened by the spirit of revenge [...] is itself a frightful despotism,” and Adams said that the “division of the republic into two great parties, each arranged under its leader, and concerting measures in opposition to each other” ought to be “dreaded as the greatest political evil under our Constitution.” Nevertheless, they lined up on opposite sides and started the long war that has gotten us to where we are now.

Because everyone wants to have their cake and eat it, too.

The world has always been about the worst of two evils, better the devil you know.
It’s comforting for society in general to behave that way, the meek shall inherit the earth sadly.

I think you hit the nail on the head when you said: “It’s a way to distract from the subject at hand, to distract from discussing the morality of the action.”

One reason is the difficulty people have in defending Trump. It isn’t possible to say he doesn’t lie so instead his supporters say “so what, all politicians lie”. Instead of praising Trump as a fine upstanding citizen they say Hillary should be in jail. It leads to a collapse of standards of behaviour in public office which is not a good thing.