In My Hero Academia, over 80% of the population has the special ability known as a Quirk. Superhuman abilities are so commonplace that it's more of an issue if someone doesn't have a Quirk but every once in a while, one manifests that defies all understanding. Some examples include Star and Stripe's New Order, as well as UA's Principal Nezu. His High Specs is one of the rare instances of an animal manifesting a Quirk, so how exactly does he have one?
While they might not be a majority, a significant number of people within My Hero Academia possess various types of heteromorphic Quirks. Transformation abilities, prehensile extra body parts and even full-on animalistic features are a few of the ways this type of Quirk presents. They prove that the genetic makeup of those living in this world can be quite different from "regular" humans.
Quirks were hailed as the next phase of human evolution in My Hero Academia. Even though they've primarily been found in humans so far, evolution has never been unique to one species. Just as humans grow and adapt to changing environments, so too do any other animals. Perhaps the catalyst that sparked the first glowing human child affected other species as well and resulted in the Principal Nezu every UA student loves and respects. After all, very little is known about the origin of Quirks as a whole. As Nezu's background or family hasn't been explored in-depth, there is no way of confirming or denying this theory.
What is known, however, is that Nezu is regarded as an anomaly even within MHA. Human scientists conducted many experiments on him in his youth in an attempt to understand how he manifested a Quirk, but to no avail. The experiments were most likely unethical as they seem to have left Nezu with a slightly sadistic streak. While he's normally a polite and charming fellow, he does take a little too much pleasure at the prospect of wielding his intelligence against humans in tests similar to those he might have undergone.
That said, Principal Nezu isn't the only animal with a Quirk in My Hero Academia. In the spin-off series Vigilantes, a villain known as Monster Cat possesses a Quirk that allows it to fuse and control objects it enters from within. However, unlike Nezu, apart from its remarkable Quirk, it is like any other regular cat. Its intelligence isn't any higher than average and it is incapable of communication with humans.
Despite his terrible experiences with humans, Principal Nezu continues to use his Quirk for the good of all mankind. His unparalleled intelligence is devoted to training up the next generation of Pro Heroes through holistic education, and his students at UA are his top priority as he's demonstrated many times. Nezu's strategy does seem to be working as the two greatest heroes, All Might and Endeavor, are both UA alumni.