IIRC, Harry thought through similar issues with respect to having a pet owl in the early chapters and rejected it on ethical grounds. Perhaps he is generalizing that to all pets.

If so, though, I don't think he's correct to do so. A pet that is (assuming Parselmouth works this way) only social when it's with me and not when I'm absent has a very different set of ethical costs than one that is social even when I'm absent.