Although I couldn't personally eat a cat (or dog) I think it's more about social norms than what animal it is. I believe that most, if not all, types of animals have the ability to connect to humans. We connect to cats and dogs in this country (USA) because they are the most common household mammalian pets, so the idea of eating one seems abhorrent. If eating that type of animal was accepted by the social norms of a person's society I think it would be perfectly normal for a person to eat them, if they chose to eat meat.
There are other types of animals eaten in various parts of the world that many wouldn't eat here, or that used to be considered non-edible and are now an extravagance. Lobster used to be a poor man's food. Possum seems gross to many.