I think you read my point too strongly. My point is not that a relationship to pets is the distinctive aspect. Nor that the cultural norm around this is relevant. What I mean is that empathy is the key and the subject of empathy is malleable. I don't know how empathy find its target but I assume that it is a process that involves pattern matching, preferrences and a lot of learning. This means that complex distinctions seem quite plausible to me. If you can learn to distinguish between dogs and pigs and between my pet and other persons pets you probably also can learn to distinguish between pet-rabbits and those in the supermarket.