"Any omnivores better be happy eating whatever[1] and better be super worth it[2]."
1: Narration over pigs in a pen.
2: Narration over a dog pulling a human on a skateboard.
Cats... aren't fully domesticated (well, there's debate). I don't remember the source, but I do remember one study looked at how well dogs and cats dealt with life when humans were removed from the equation. IIRC, dogs are iffy. Sometimes they do okay, but a lot of their behaviors have evolved for cohabitation with humans, so don't work as well when humans are removed and a pack functions purely with dogs. Cats have much less problems, and it was claimed this was because of their only partial domestication.
Another way of looking at it is that being a pet does not infer domestication. I can have a pet rat, rabbit, hamster or one of many different species of bird. That doesn't mean that species is domesticated (it may have a natural timidness that lends itself well to being a pet, at least more than an aggressive animal might). That's not to same some level of domestication may not have been achieved with some breeds of those animals (e.g. rabbits).