Are girls inferior because Eve ate the fruit or were they always inferior?

I've heard girls are inferior and biologically burdened by sex with us because Eve ate the fruit but it seems girls were always inferior because they were made from us and for our pleasure and company and we named them like the other animals. If Adam exercised his authority over Eve and punished her for eating the fruit instead of submitting to her and eating the fruit himself then humanity wouldn't have been cursed.
Are girls inferior because Eve ate the fruit or were they always inferior?
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