Actually cats does not love to eat a mouse..... but a cat loves to play with the mouse.  Since a mouse would of course run for their lives when a cat chase them... or hunting for them.... the cat would do anything to catch them. Same with the birds!

I cat is a natural hunter and when it sees a mouse its instinct is to chase after it and capture it. It is the same with other animals such as birds. They are just doing what they would do if they lived in the wild.

Mice are a perfect food item for cats. They are small, easily eaten, contain all the nutrients a cat needs, readily available as they reproduce rapidly, and found in most every sort of environment including the desert type environment the cat was developed in.

What attracts the cat to the mouse is its quick movement and high pitched voice and possibly even the tail. A housepet cat will often respond to the high pitched noise of us squeaking our lips to catch their attention and is usually very interested in dangling strings or toys that resemble mouse tails or bodies.

This is all 'built in' to the cat to be interested in these things to promote its survival in a wild environment.

As we humans like to store things that mice like to eat (food for example) or nest in a natural partnership has developed between cats who like to eat mice and humans who'd prefer mice didn't eat all our stuff!