Why do cats bring us their mouse catch and leave it at the door  ?

This is nothing that you need to worry about. It's known as what's called 'bringing a gift' and is a perfectly normal cat behavior. 

Know however, that it may not only be a mouse which a cat brings. They may also bring other small animals, like a rat, a small bird like a blackbird or robin, or if they have access to an area of water like a pond, a frog, toad or fish.

It may be absolutely disgusting to a person, but cats do this for 3 different reasons:-

- despite cats being domesticated pets, they still have a natural predator instinct, and so hunting behavior is part of this.

- it's also done out of love and affection, similar to a little child drawing a picture and then giving it to their parents. This is because the cat wants to share their 'catch' with you.

- it's naturally done in the wild to teach juveniles about hunting, or to teach other individuals who they live with about hunting. This is why it's a more commonly seen behavior in female cats, especially those who haven't had kittens, or were spayed before having kittens.

Due to this being a natural behavior and out of love, it must never be punished. If a cat does this, the ideal thing to do is to stroke the cat, say 'good girl/boy' or 'good cat' and give them a treat, then take the 'gift' and dispose of it, preferably somewhere the cat cannot see you do so.

Hope this helps.

They lubs you and are bringing you treats , a show of their affection lol. Gross but cute sorta \ 0,o / . Sometimes you may get birds too, jazzy .

Well most domestic cats are well fed and when they catch a mouse the cat is  probably not very hungry and won't eat it so it brings it home. Most farm cats or barn cats rely on catch for a meal, not all of the time but they are usually hungry.

For two reasons:

it's a feline way of saying "look what I can do!"

cats don't think humans know how to hunt and of course don't know about supermarkets

It is a gift for their owner, since they notice that humans aren't very good at catching their own mice.

It's a gift. Enjoy!

It is actually part of their instinct to take their catch to a place of safety before eating it.  Cats want privacy and safety before settling down to eat.  These days that safe place is home.  So they're driven to bring it home, but then usually they lose interest because they aren't actually hungry.

We love to think they're trying to provide for us useless hunters.  It isn't so, but there's no problem with viewing it that way.

It is a present for you.

You are their family so they bring you a gift of food. If my cat brings in a live bird I do my best to rescue that bird and set it free again outside. My cat once brought me a big black raven and placed it by my bed, it was a bit of a shock but I put it out for the fox that night lol. 

Because you are part of their pack/family.  In the wild, a cat who is with a group would bring kills back to the group.  Though...likely he ate his fill first.  It's their natural instinct.