The Patriarchal Society may once have been a thing, but I think my generation killed it (at least in the West) in the 1960’s. If you think it still exists and needs to be killed I think that makes you a Rationalizing Feminist rather than a rational one. A rational feminist would be a humanist, ready to meet other humans and judge them by their behavior, personality and competencies, not just by their gender.
That appears to be what you are saying in “Let’s set the example so that billions of women around the globe can be individuals. It costs no money and you can do it in almost any interaction you have in your everyday life. Instead of a Patriarchal Society or a Matriarchal Society, let’s set the foundations of a Human Society.” It took a long time for you to get to the point, but you got there in the end. Be careful with new norms, though: some of the gender norms are necessary for protection of both genders from each other. I hold doors open for men as well as for women: I’d rather do that than virtue signal by not holding the door open for women.
I used to call myself a feminist because I thought female equality was a obvious truth, back when this wasn’t a popular thing to believe, but the title has been so dragged in the muck by the man-hating extremists you refer to that I no longer apply it to myself, or to anyone I respect.