But even that's only a temporary "ownership". (Besides which, the question was in regards to pets kept as companions, not livestock kept for food.)

C.S. Lewis raised an interesting point in The Screwtape Letters about the double-edged nature of the idea of "ownership": children can either think of "my" teddy bear as "the bear with which I share a special bond of friendship", or "the bear I can pull to pieces if I like and no one can stop me".

I think far too many of us tend towards the latter interpretation of "ownership", and I think it would better things considerably if we had more of a "borrower" attitude towards everything: the land, the planet, each other, etc etc etc.

I think the meat of the matter (pardon the pun) isn't in what you call it. Given that plenty of people abuse their children, about whom we don't use the term "ownership," I think the issue is the human capacity for rage and cruelty. That's not to say that in general I think what you call things doesn't matter; I just think some verbal distinctions imply a subtlety that the real world totally lacks, and this is one of those cases.

I don't think their main issue is the legal definition, though; I think their main aim is in the way that people think about their relationship to their pets. "Guardian" certainly implies a weighty responsibility: you guard your pet from harm, disease, hunger, the elements, etc etc etc.

Of course, if the pet in question is a cat, then we all know the proper term is "slave". But cats are, as always, a law unto themselves.