I honestly think the hardest part of explaining cat behavior is how chaotic they are as a species. You can explain A cat's behavior, but it's harder to explain all of them. My cats, for example, completely understand knocking over (even large) containers to get food, understand that turning door knobs will open doors (thankfully their lack of thumbs means they usually don't have the grip to pull it off), but fail to understand that sitting ON the closed food container means I can't use it to feed them.
Ive read that not only are cats more recently domesticated than dogs (like, by an order of magnitude of years, with dogs domesticated 50k-80k years ago) but that domestication didn't involve OUR deliberate breeding of them outside of recent centuries, so the traits selected for are more about compatibility (for their benefit) than for anything we explicitly want. My personal theory is that housecats are often from such small genepools (that haven't had a lot of recessives weeded out of them yet) that cats tend to be this mix of genius and idiot and weird, so it's very hard to extrapolate generalities from a few specimens. But that theory is likely worthless.
I applaud you for trying to explain this. You could be completely right, or wrong... We're talking about cats after all.
But when he is outside asking to come in, as soon as I open the door, he runs right inside. Perhaps it is because the inside environment is very stable for him with no threats ever so he trusts it.
He does this freezing behavior when guests enter the house. My housemate's cousin brought a huge dog for an afternoon visit. My cat froze entering the living room, detecting an unknown threat, and turned around again and went back to my room.
Gwern published a nice article about cats recently: https://www.gwern.net/Book-reviews#cat-sense-bradshaw-2013-a...
My cat definitely, however, is unaware of the idea that the environment around him can be changed, and isn't static. He can figure out how to open doors, and that if something is playing dead it will run when he knocks it from a shelf, but those are the limitations of his ability to interact with the environment.
He's smart enough to know his treats are kept in a small bin on a shelf in my desk, that weighs under a pound, and is covered by a thick sheet of paper. He could knock the whole thing to the ground and get all the treats he wants. But because it looks too big to be an eatable animal playing dead, it simply doesn't occur to him he can push it open to get the treats inside.
That, I think, explains a lot of their behavior. The cat will scratch at the door to go outside. But when I open the door, he needs to take a moment or three to re-situate himself in his new environment, for him, his entire environment just changed unexpectedly. If I then poke my head through the door, he'll realize that its open now, and run through. But if I don't, he needs to re-assess his entire locale, realize that the open door means its passable, and ignore his confusion for how his environment changed so rapidly.
This is true with a lot of things. He'll complain that his litterbox is too dirty. I'll clean it. He'll leave the litterbox, and go do something else. Later, he'll come back, find that its clean, and go to the bathroom. Its not that he was being an asshole, he just knows enough to have figured out that meowing next to a dirty litterbox results in it eventually being clean, but doesn't seem to recognize that the action of me scooping in there is what is actively changing the environment, he needs to rediscover his litterbox as clean 1-5-10-15 minutes later.
etc
You can use this to your advantage to play games with the cat, interestingly enough. I play with him with this thing: https://www.chewy.com/snugglycat-ripple-rug-cat-activity/dp/...
Some days, he gets bored with it. So I unvelcro it, change its shape, and start playing again, and suddenly, its an entirely new toy, and he gets excited again! lol