the obviously false notion that "the opposite of love is indifference"

Perhaps the word "opposite" is not the best one, but I think it's about this: in some metric, loving people and hating people is closer to each other than either of them is to the paperclip maximizer's attitude towards humans. In HPMOR universe, a magical paperclip maximizer could shoot AK like a machine gun. Instead of replacing one emotion with another emotion, it's replacing one emotion with an absence of an emotion.

Instinctively, people sometimes prefer to be hated than to be ignored. For example, children trying to draw attention to themselves by behaving badly. There is some "recognition" in hate, that indifference lacks.