There are some reasons why Chinese people do not eat cat and also ban to eat dog. But I only know two and want to share with you guys.
1. There are 56 Peoples in China, and the majority is Han People. There is a special group of People named Hui People. They believe in Islam. Islamites do not eat predators or omnivorous animals, including pig, dog, cat, snake, rabbit, etc.
2. Sometimes people are superstitous in China. We like to take certain kind of thing to stand for another thing. Cat in Chinese pronounce mao. You know the first Chairman in China is Chairmao. His family name is Mao. Though the tone of Mao is a little different to mao(cat), it is very similar. So at that time, cat standed for the Chairman. In the past, if people wanted to eat a cat--mao, it means that they wanted to kill the Mao--the Chairman. They would be seriously punished. People had to treat cats well at that time. So until now people still hold the idea not to eat cats.
These are some of the reasons why we do not eat cat or dogs. I hope these two reasons will help you clear your doubts. ^_^