There are several possible reasons why a cat might carry its kittens around:
Lack of security. After living in one place for a while, a cat will always leave some scent, which may attract predators. Therefore, the mother cat will instinctively want to find a safer place, so she will carry the kitten to another place.
Trying to please their owner. When a mother cat trusts her owner, she may bring her kittens to them, hoping they will pet them.
The living environment is too poor. If the owner provides the cat with a poor living environment, such as a damp, dirty, or poorly ventilated environment, the mother cat will carry the kittens to another place to live.
