Cat on a string in front of a restaurant

In China outside some restaurants they have grubby cats on very short strings. From my western point of view I find this cruel as I keep cats in England. The Chinese seemed incredulous when I told them that if you fed the cat well it would come back to the owner. What I have to wonder about is, is this cat on the menu? I've seen dogs hanging up at outside butcher markets.But, I have to keep a sense of cultural relativism. After all Europeans eat pig, which is often considered an intelligent animal, and is considered disgusting by Muslims.

When confronting a Chinese lady about eating dogs she explained that in the past when people were starving eating the pet dog was the least of their worries. And, I have to admit I see her point. People ate the bark of trees and some students have even informed me that dead bodies were eaten. Though this sort of fact is strictly hush, hush.