In this culture, we anthropomorphize dogs (and, to a lesser extent, cats) so much because they are widely kept as pets. They are, to an extent, honorary humans. That's the difference between hunting deer and killing dogs -- mainstream America regards Bambi as, while very cute, still essentially an animal. But we regard dogs as our surrogate children.
Killing a person is obviously a much worse crime than killing dogs -- even a lot of dogs -- and I think most Americans would at least pay lip service to that. But I bet that for half of the people in this country, grotesquely mistreating and killing dogs is more viscerally repugnant than killing a man, similar to how pedophilia is commonly regarded as a much more monstrous crime than simple rape. The law just reflects that irrationality.
(Disclaimer: I'm not a dog owner, and don't feel particularly strongly about them, at least in general -- some dogs I really like, and others I can't stand. Just like their owners.)