Probably because cats and dogs are dedicated carnivores. Pigs and chickens are omnivorous, but when we raise them for food we tend to feed them a vegetarian diet. In less wealthy countries cats and dogs are eaten......
Our main farm animals are vegetarian. It's possible that our dislike of eating other carnivores has good reason behind it, as the more meat eaters there are in the chain, the more concentrated certain toxins in the liver may be - I think this is the case with polar bears - don't eat them - but on the other hand, don't let them eat you

On one of the explorations trying to find a way through the North-West Passage, the entire team died because they ate nothing but Polar bears.
As for eating half developed chicken embryos - no thanks, I don't fancy all those bones and feathers. Also, having been raised on a turkey farm, the eggs with dead embryos in were rotten
