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you're WAY off on mid-defining 'power'.
you say: "I want you to do a little thought experiment: compare what you would think the success rates would be for a guy simply going up to a random girl and saying "I want to have sex with you", and a girl doing the same to a random guy. Until feminists agree to acknowledge that there would be a disparity (read: imbalance of power) ..."
NO!
If a guy says that, it's sexual AGGRESSION in a FRIGHTENING WAY (unless it's a joke, in which case that would be freakin hilarious and a guy I'd talk to).
A girl can't (easily, normally) have the PHYSICAL and SOCIAL POWER to Injuur, Demean, Sexually damage, or Rape a guy.
A guy can EASILY do those things to a girl, usually while blaming the girl.
There's a very instinctive, biological reason women naturally shy away from guys saying something like that- It's the MAN taking POWER OVER THEM.
Not the power to 'GRANT SEX' but the power to KILL or INJUR or RAPE or PERSONALLY DESTROY.
A guy has no such fears of girls. Their only thought would be 'Yes! Sex! Screwing something other than my right hand!' Because instinctively there's no physical fear.