Interesting. I think he wants something that you've had. I do think cats look to us for what's important. We don't know what they're actually thinking, of course, but I suspect cats think of us in one of three ways: That we're their mate, or their caretaker, or that they're our caretaker. I tend to think they think of us as their caretakers, since we deliver them food, and anything the more dominant animal has, the cat wants a piece of that. Like when they rub up against us, they're getting our scent against them and it makes them feel safer. With any animal, but especially cats, you can boil down almost any behavior to a survival instinct. Even playing. It's the way they practice hunting.
When a cat curls up on something, are they looking to make their bellies warm or cool?