The thing you have to realize is that the most ancient domestic cats are only about 6,000 years from wild, and in some modern breeds, only about 3 generations, compared to dogs, who have been with us for over 12,000 years.
And unlike dogs, they are not pack---social animals, but forming a pride, at their most social. The thing about pack behavior is that it comes sometimes pretty close to primate---the dominance thing, etc. Cats? Nope. Everything in our primate ancestry says, Assert dominance, get control---and it doesn't work with felines of any size.
Recall, too, that most of the really small cats are solitary hunters like the leopard or the tiger, not really prone to group living. So the ancestry of the modern domestic cat is really against any group structure. You can get two cats to share a household, if you do some careful supervising during the introduction, but people who pack multiple cats in [the stereotypical cat lady] in the theory that this lets them 'be cats' is not doing the cats a favor. They want their own relaxed territory...which should be pretty large, within the house [as soon as they grow up and learn manners!] and they shouldn't be having to watch their backsides against snipers at every turn. You can watch kittens in such a household treading a very thin and wary line of invisible hostile boundaries and not playing and acting the fool, as kittens should: this is the kind of situation I got my own Ysabel from, and it left its mark. I had to teach her how to play after she was near adult, and she still hasn't quite distinguished that activity from Mortal Kombat.
The main thing is---as primates we 'discipline' with swats and scream at the offender. Not great with kids, but absolute worst thing you could possibly do with felines---who will take you up on a fight, and, what is worse, remember and 'get' you later. Even sweet Ysabel will wait until you relax, then 'get' you for some misdeed.
I love 'em, but they have their ways, and you just have to respect that.
What can you expect from a cat? Certain basic behaviors are teachable. Contrary to her every instinct [Siamese climb], Ysabel knows not to get onto counters, tables, especially in the kitchen; she knows she can sit on any table next to a chair, can be on a chair arm, but needs to move if someone wants to sit down.
She knows not to scratch furniture, but to go to her scratching post if her claws have a snag.
She comes when called [She's Siamese: most breeds won't.] She follows almost every step I take all day long, unless she knows I usually make a short U-turn. She knows her name. She knows "no," "no claws", "stop that," and "Get down," "Good girl," and "settle!" And on the road, she knows: "Get in your cage."
She does not bite and claw when picked up...unless picked up by somebody not of this household. This is a problem, but I don't have enough subjects whose fingers I want to risk to train her out of that.
She will not sit on my papers, or mess with papers.
She will not take food from a prepared plate until it is offered to her...even if the plate is left unattended. There is however a time limit after which she will construe it as 'abandoned,' and fair game.
She will allow herself to be picked up and set down and stay there. That's pretty rare. She gets mildly out of sorts if she doesn't get her morning brushing in her chair with her proper brush. Some cats don't like to be brushed at all.
I have had cats who: would open mouth on command and swallow a pill; would play fetch with paperballs; can find their own way under the quilts, and will allow claw-clips. I've known cats who can turn on the cold water tap---not a good idea.
They're nothing if not individualists.