I don't have any special talent of my own for knowing how cats think and behave. I just apply what I've read in articles and books by animal experts who have studied them.
Example: My current cat, Ember, is very strong willed and we used to get into power struggles when she insisted on doing things that I wanted her to stop, like getting onto the table. The more I said, "No, no," the more she defiantly hopped up there with a hostile stare at me.
Then I read about how cats communicate friendliness to each other in body language. The article said that it works with cat and human communications, too. Cats will blink slowly at each other to indicate an absence of hostility. It can mean affection, or friendship.
So when she got mad at me for saying, "No, no," I did the slow blink at her a couple times. She calmed down and stopped thumping her tail. After a minute, she slowly blinked back at me. Blinking back at me meant, in cat body language, "OK, I understand. We're still friends."
She started initiating the slow blink at me when she did something that she knew I didn't like. It was like saying, "Oops. Still friends?"
She has not lost her feline independence. She's just more civil about it and more cooperative with me now that we've established that we are friends who mean no harm.