The cat may put up a fight, but a healthy uterus has a thick lining for protecting itself against teeth and claws. Through the power of kegels the cat is quickly subdued, brought up into the body where it's stored for later.
The cats are later used to attack other women. This is how true ladies establish dominance in social packs. The attacker releases her feline and the defender does the same. They battle in a "cat fight". Whoever's cat is the winner gets to continue to climb up the social ladder.
A woman can be challenged at any time, so it's not only important to always have a cat up there, but also a strong one. This is also where the street term "pussy" comes from, and why less hygienic women's vaginas smell like fish.