Would you eat a cat?

Someone recently told me that even though they would not eat a cat or dog, they think that because China is so overpopulated, anything with meat is a meal, and that it is no different eating a cow than a cat. They said it's not fair to separate one life from another.
I could not kill any animal for food. If I had to, I would become a vegetarian. But I feel that it should be much harder for someone to kill a cat for food because they connect with humans and can love and be loved by people. Is it me? I mean I was horrified as a child seeing a live lobster being thrown into a pot of boiling water. I could not stop crying.