In Genesis, God puts a curse on all women. Would refusing to 'cling to this dichotomy' make the curse go away?
You have conceptualized it as a curse, but is it really so?
Eve has come from Adams rib or heart - depending on your definition of 'eve' - and not from the dirt. She is more purified than the man, the result of another evolution after man. She has also been more open to the serpent - always a sign of wisdom in the ancient traditions, and even for Jesus - and thus questioned the lack of justification from God - she thus ate the fruit from the tree of knowledge. We see this advancement of the female today in psychiatrists evidence that the girl matures around 3 years faster than the male.
Now she goes and tells Adam to do the same, but after doing so, he is the one that is filled with guilt and says he has feared the wrath of God for disobedience. To this day, it is very easy for a man to join the army or police force and do his duty without questioning anything. He will actually feel worse if he hasn't obeyed than in what the instruction has caused him to do. He is far more simple minded than the woman, yet he has become far more strong. This has been necessary because his basic instinct is to compete, the woman needn't be so strong because she simply has to wait and allow the winner. This has caused a complex in the man, he believes himself superior to the woman based on this fact alone. Now we see all types of stupidity in our treatment of women throughout the world, we can force them to wear attire that hides them from us, we can keep her in the house, all manner of things. It is really our impotency to control our desire that has caused this though, it is our weaknesses that causes us to need to prove our strength - it looks paradoxical but non-the-less is the case.
This too is the way of the inner world, at first you will attack, you will try to rape God into presenting himself to you, or you will be aggressive in your insistence of God being a reality. Then eventually, when you see the futility of this, you become receptive, essentially female in your way, you simply wait and allow, inviting but not chasing, then there is a possibility.
People should not take these things at face value, that is how stupidity comes in.