It's not about hurting them, it's about hurting you. Just as in the CS Lewis quote hilzoy used, the more you let yourself think of other people as "not human" the more of yourself you cut off. There is no "get out of species free" card (and I hear the Martian citizenship residency requirement is a *bitch*).
When you say "this (group, behavior, whatever) is not human", you are not telling the truth. In addition to my moral reaction, I'm a biologist, and I invariably find that the behavior people are most ready to label "inhuman", "not a human being", etc., is in fact *precisely* human. Frequently-made comparisons are insults to weasels, snakes, and things that live under rocks. There are no "vicious" wolves, because wolves have no vice -- though there may be vicious dogs, because we've made them into half-people, psychologically.
When you label someone "inhuman", you are stating "there is no way that could be me, there is no commonality between me and that behavior." If there's one thing we learned in the 20th century, it is that this is a delusion. It is *always* us, it is always pure 100% human behavior with no non-human ingredients going on.