Altruism is one of the most obscure human instincts. The rules of evolution state that living creature's purpose is passing down his/her genes and disposing of competition, so that one's descendants will be situated better. Therefore, the voluntary help we are often willing to give each other without prospects of reward has no basis in the evolution, as giving anything away lowers our own chances of surviving.
However, altruism is widespread among humans, as a virtue praised by all world's religions and ethical systems, as a common sight on streets, as a rule of good manners and as a force that makes sometimes incredibly rich people give large sums for various charities. On the other hand, in popular opinion it is a virtue unpracticed by animals other than humans. note This has led to the glorification of altruism and its perception as a "human virtue".
Now, let us consider what a phrase "human virtue" means. Obviously, it is something exhibited by humans, and humans only, therefore exalting them above animals. This is a positive value, in contrast to so-called "animal instinct". "Animal instincts" are rapacity, lust, hunger and survival at all costs; "human virtues" are love, joy and altruism. "Animal instincts" are perceived negatively - people who display them are considered brutal, selfish and dangerous to society. "Human virtues" are seen as positive values and the qualities of a good person.
Pet the Dog trope exploits this contrast. The evil character is often seen displaying "animal instincts", as s/he is largely motivated by personal gain and exhibits absolute lack of any empathy. This makes evil person very inhuman and more animal-like, which carries a pitfall of its own. By reducing character to a human-shaped animal, author involuntarily signals us that character is animal-like in more aspects and so less cunning, intelligent and clever. While that kind of person can still present a significant physical danger, s/he is not much in the way of psychological challenge.
Of course, enemy with no redeeming qualities can be psychological challenge. However, presenting him/her as absolutely evil makes readers harder to believe it and turns him/her into more of a rabid monster that should be shot than actual person.
Showing a Pet the Dog moment of evil character humanizes the character. By displaying the most human of virtues, altruism, we are being proven that we see not a caricature, but an actual sentient, intelligent creature with more than one dimension. This both deepens the antagonist and makes us treat him as a serious threat rather than generic monstrosity that can be taken down by directly applied sufficient amount of brutal force. This also lays ground for Character Development of a villain that makes us wonder about his/her future actions and hints a possibility of turning him into Anti-Villain or even Heel–Face Turn. And above all - this makes the story more interesting.
The dark side of this trope lies in the Unfortunate Implications—a "cute", "helpless" character is often called upon to act as the "dog". So, then, What Measure Is a Non-Cute? Who gets saddled with the Distress Ball? Why is that an otherwise evil character showing kindness to someone, anyone, is taken as a given sign that they are not so "bad" after all? Why not this kindness the very motivator that drives them to villainy?
