Does equality mean equal responsibility?

I can slap him but if he slaps me, he's abusive. if I cheat, he wasn't good enough, if he cheats he's trash. I can yell at him but he can't yell at me. I can flirt and if he's mad it's because he's controlling. If he flirts, he's a man hoe. No. Equality means equal responsibility.
Does equality mean equal responsibility?
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