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I could agree with you, but why call this culture "patriarchal"? I'd call it "animalistic" if anything. "Patriarchal" involves male/female duality and ascribes certain features to men and women that they might not currently be comfortable having. If someone is dominating, let's just call this person "dominating", not "having male features." If we go down the rabbit hole of patriarchy, in the end sooner or later someone starts accusing men for all evil, and this is one of the greatest misunderstandings of our age.