@OP, that's ridiculous. Cats are never butchered in Korean markets. Koreans don't eat cats (there's a very rare tonic made from cats, but chances of you seeing it are close to 0). Dog meat is sold in some of the very old school markets, but it's not always obvious and I've never seen it being butchered. I've lived in Korea over 3 years. I've been living 2 blocks from an old school market for over a year and go shopping there 3-5 times a week.
@Kraziekatie, I always see pigs getting butchered in the markets around me in Korea. A number of the butcher shops will have the pigs hanging on meat hooks behind the counter. They're not salughtered in the markets, but they are definitely butchered there. Rabbits are eaten in Korea, just not that much. There's a restaurant on my block that serves rabbit soup (and boshingtang and other specialties). I wouldn't say dog isn't common. It might not be out in the open, but there's plenty of restaurants around. Lots of people don't eat dog, but a fair number of folks eat it fairly often.