You should thank the cat.
Theory 1: The cat is trying to teach you how to be self reliant.
The cat *will* stop if it sees you successfully stalk and catch something.
Theory 2: The cat is grateful that you provide food and shelter and is attempting to contribute to the communal food supply. (Yes, cat society *does* allow formations of colonies that help each other out. Your family is the cat’s “colony”.) It is bringing the prey back still alive so it will be fresh for all to partake in.
Crazy Nimh cat is absolutely ecstatic when the humans chase live prey.
It seems to be some form of primitive feline entertainment to him.
He almost seems to be laughing at us, even after catching the ‘invader.’
Though getting him to not try and assist in ‘battle’ with the pest creatures outside proved difficult until we moved.
Once he heard the coyotes outside the window, he decided not to try to assist anymore.
It was hard to chase off possum and worse when you have the cat in there trying to get his own digs in.
(Punt a possum sometime with your cat trying to claw the things face off, not easy to do with the cat in the way.)