That thing about how cats think humans are big kittens is a myth, y’know.
It’s basically born of false assumptions; folks were trying to explain how a naturally solitary animal could form such complex social bonds with humans, and the explanation they settled on is “it’s a displaced parent/child bond”.
The trouble is, cats aren’t naturally solitary. We just assumed they were based on observations of European wildcats - but housecats aren’t descended from European wildcats. They’re descended from African wildcats, which are known to hunt in bonded pairs and family groupings, and that social tendency is even stronger in their domesticated relatives. The natural social unit of the housecat is a colony: a loose affiliation of cats centred around a shared territory held by alliance of dominant females, who raise all of the colony’s kittens communally.
It’s often remarked that dogs understand that humans are different, while cats just think humans are big, clumsy cats, and that’s totally true - but they regard us as adult colonymates, not as kittens, and all of their social behaviour toward us makes a lot more sense through that lens.
They like to cuddle because communal grooming is how cats bond with colonymates - it establishes a shared scent-identity for the colony and helps clean spots that they can’t easily reach on their own.
They bring us dead animals because cats transport surplus kills back to the colony’s shared territory for consumption by pregnant, nursing, or sick colonymates who can’t easily hunt on their own. Indeed, that’s why they kill so much more than they individually need - it’s not for fun, but to generate enough surplus kills to sustain the colony’s non-hunting members.
They’re okay with us messing with their kittens because communal parenting is the norm in a colony setting, and us being colonymates in their minds automatically makes us co-parents.
It’s even why many cats are so much more tolerant toward very small children, as long as those children are related to one of their regular humans: they can tell the difference between human adults and human “kittens”, and your kittens are their kittens.
Basically, you’re going to have a much easier time getting a handle on why your cat does why your cat does if you remember that the natural mode of social organisation for cats is not as isolated solitary hunters, but as a big communal catpile - and for that purpose, you count as a cat.