Nearly all Western societies (and most Eastern ones) are demonstrably rigidly male-dominated. Of course there's variation in between Iran and Italy on that and are other things going on in all societies other than just the socio-political structure - and I didn't say that there weren't, but it's madness to act like that doesn't exert a HUGE amount of influence. All societies are complex and multi-faceted, but patriarchal dominance hierarchies are still essentially structured in the same ways, with the same components, leading to basically a lot of the same problems with inequality, discrimination, and violence.
As one example, all Western democracies have people under stress, mental health issues, and poverty, and yet, the US has many, many times the amount of gun deaths as other countries due to specific factors related to easy gun availability and culture.
But at the same time, from a systems science perspective, as Eisler notes, "All societies are patterned on either a dominator model - in which human hierarchies are all backed up by force or the threat of force (patriarchy) - or a partnership model with variations in between."
And don't try to tell me that the US isn't a rigidly male dominated society because the data to support that it isn't there - despite some improvements in the past few decades. It's illegal to pay men and women differently for the same work, and yet that still goes on rampantly. Women have to sue nearly every day to get their legal rights enforced, and men are given the most lines in nearly all movies and television shows, even if the main character is a woman, as just a few examples. I could quote you statistics for days, but I don't have the time, and I also shouldn't have to do your homework for you.