Why Isn't the Cat in the Chinese Zodiac?
Twelve animals, no cat. There are two answers — one from folklore, one from history.
The folk tale
In the story of the Great Race, the Cat and the Rat were friends who planned to cross the river together on the Ox's back. The Rat pushed the Cat into the water — or simply never woke it up — and the Cat missed the race entirely. This is offered as the reason cats hunt rats to this day.
The historical reason
The more likely explanation is timing. The zodiac took its current form well over two thousand years ago, and the domestic cat is generally thought to have reached China later, along the trade routes, after the twelve animals were already fixed. The animals in the zodiac are the familiar farm and wild animals of ancient northern China.
The Year of the Cat elsewhere
Vietnam uses the Cat instead of the Rabbit as the fourth sign — so a Chinese Rabbit is a Vietnamese Cat. One common theory is that the old Chinese word for Rabbit sounded like the local word for Cat when the system was adopted.