Nothing to do with pets, but in Korea there are places that serve dog. At least it was the case when I was there 20+ years ago. But, of course they're not pets, they're farmed like any other livestock I would expect, and these places were not exactly commonplace even then, so maybe now they're just not a thing? I've not really looked into it.
Now, saying "x" people eat pets is likely just what others have said, a slur used against whichever subset of people is the target of the month. Maybe it once had roots in facts like those I've mentioned, but they're far removed from them now.