It does not say she has to "obey" you. Sorry, mate, but I'm sure you'll survive without a slave somehow - it says, "and he shall rule over her."
But, bad luck, Jesus died on the cross and wrecked it all. What a shame. So, Isaiah 53, he took up the suffering mentioned right there in Genesis. He redeemed women (and men, but we're discussing women here) from the curse of the law by becoming a curse for us.
Galatians 3. Let the redeemed of the Lord say so. Not only that Jesus said the gentiles like to vie for power and lord it over each other - but not so among you. Instead, serve as a slave if you want to be a big shot.
Amazing, women are redeemed from the curse/consequence of both pain in childbirth and male domination! It is fun meeting people who live this way. They really are liberated. They're redeemed!