Why does my cat bring home dead mice but not eat or let me touch them?

In the wild, the mother cat teaches her kittens to hunt by bringing back dead prey for them to play with, She will occasionally bring back injured ones as well to teach them how to hunt. It's thought that cats will bring back dead animals to their owners as they know they can't catch prey themselves and are trying to teach them to hunt.

An indoor/domesticated cat likely would not eat a frozen mouse. He or she may play with it, but that's all. Feral cats can and do survive solely on a diet of small wildlife. They've been "taught" by the mother how to hunt and kill small prey.

They are leaving you presents! They are gifts, and it's showing you affection. They are grateful for the food. I wouldn't stop feeding them, and since Feather is kept indoors, this won't be a problem for her.

If your cat didn't eat it, health risks would be minimal. The main secondary issues from hunting are tapeworms (if they eat the mouse) and issues from fleas (so I would apply a good prevention like Revolution of Advantage Multi). Another consideration would be to make sure you don't have rodenticide poisons anywhere because if they caused the mouse's death and then your cat ate it (or a future mouse!) then they would also be exposed to it!

Obviousl she is a very good mama. He will actually only eat as much as he wants. Mama cannot make him eat. She is apparently still trying to teach him how to hunt and he just may be a little bit slow to learn. Just remove the dead prey as you find it. eventually she will stop.

Mice are not an unusual snack for cats and rarely cause any symptoms at all other than occasionally vomiting. Monitor for any severe vomiting and report to your vet if this occurs. If mouse bait is used, there is a possibility she may be exposed to this so monitor for any other unusual signs

I think that if he is doing well on his current food (the Hill's or the Natural Balance) then they are fine to continue. It is unlikely changing his diet will change his habit of killing birds/rabbits/rodents. It in not likely due to hunger it is likely something he enjoys (as awful as that may sound to us!) and is a natural behavior for him. I don't normally recommend raw diets as there are risks when handling raw meat to the animal and to the owner (such as salmonella and e. coli). I think if you want him to stop killing you will have to either keep him inside, let him out in an enclosure, or you can try putting a bell on his collar in an attempt to warn off small critters (just be sure that it is a quick-release collar so he doesn't get himself hung on something and choke).