Our society is in flux, and as you pointed out, they always are. But patriarchy is alive and well and is not just about men having power and rights over women. It’s a social system that is a dominance hierarchy and the US (and most of the world) still operates very much out of this system.
Your example of Rosie the Riveter is an interesting one, because when women were needed in the workforce during the war, it was considered fine for them to do so. Once men came home, those jobs went back to being primarily for men, because they were supposed to be primary breadwinners and women needed to get back to what they were supposed to be doing, which is raising children and keeping house. The fact that many women didn’t want to go back into those roles exclusively after having tasted what it was like to earn their own money did help to change our society, but there was also significant backlash against it. One of the main aspects of patriarchy is strict gender roles, and although we’ve definitely seen some loosening of that in recent years, it’s still a huge factor in our society. It’s a major component of homophobia, for example, and that is still pretty rampant in the US.
Unfortunately, all of the tropes that I wrote about were ones that I have routinely heard bandied about by men.