Here's why:
* Mammals give birth to live young. Cats have kittens, not eggs.
* Mammals nurse their young with milk. Cats have mammary glands and produce milk to feed their kittens.
* Mammals have hair or fur. Cats are covered in fur.
* Mammals are warm-blooded. Cats regulate their own body temperature.
These are the defining characteristics of mammals, and cats fit the bill!