I have two cats. For the “He is also pressing my arm alternating with his left and right paws.” called “kneading” in this thread and “tritteln” by German psychologists, there are actually two explanations:
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The “milk-walking” explanation is obviously the more popular, as this thread shows. Though I personally do not think it is the correct one all the time.
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When cats go to rest, they will prepare their sleeping place, by loosening leaves on the ground. They do so with exactly the same kneading by alternating paws, as they do for “milk-walking”, but with more use of their claws. And if you watch carefully, you will see, that they slowly walk forward while they knead, in order to cover a greater area. After they have “prepared” about 1/2 to 3/4 of their length in this manner, they will suddenly turn around and lay down. But usually you wont see this behavior completed when they knead you, because simply you wont be able to stand their claws.
However, in any case this kneading behavior just shows, that the cat feels very relaxed and comfortable. If he does it to you, he likes you very much, he feels safe around you. Nothing weird about that. Both of my cats do it to me, though one of them only rarely, but both do it equally often at their sleeping places.
As for the “nipping”. I’m German, and not quite sure if I understand you exactly. Does your cat actually try to suck your skin? Or does he just press his head (and nose) a few times against your skin, and as the nose might feel cold and wet, you just mistake it for sucking?
For the second: Pushing the head firmly against the breast, is yet another “milk-walking” behavior, and as such is found not only with cats, but with lots of mammals. But for cats, “giving the head” is also like our “shaking hands” a greeting behaviour. As cats often live a single life in the wilderness, you wont see it there very much, except with children and their mother. But as others already said domesticated cats never really grow up (especially if sterilized) you will see it quite often with them.
My two cats are not from the same mother, so they do not like each other very much, and hence never give each other the head. But they do it to me and usually right after they approached me, however, as my head is too large to be recognized as “another head”, they will usually not react to my head, but to my fist (which would make the wrist a “neck”). They often expect me to greet them with my fist, before they will join me on the couch.
So essentially this behavior indicates trust and acknowlegdement of friendly intentions.
So you should be proud that your cat does like you so much. While some will say, that all this behavior is not natural behavior, and they are correct. You should still not listen to them, because natural behavior would be to flee from humans and that is exactly the main difference between domesticated and wild animals. Interspecies interaction is very rarely natural behavior, except between predators and their prey, and you would not eat your cat, would you?
cu