Mary- the new Eve

Paul calls Christ the new Adam and many Church Fathers saw Mary as the new Eve. If you juxtapose the two responses to their "miraculous" births(the only two "seed" of a woman) you can see direct opposite reactions.
Eve says, "I have acquired(kinyon) a man with(et in heb.) God". Eve uses the term et instead of im which possibly means utility- such as I dug a hole with(et) a shovel. vs I dug a hole with(im) Dave. Im would imply partnership. So her reaction to the birth of Cain was pride.(perhaps this also explains the difference in the two sacrifices of Cain and Able.)
Mary, on the other hand, responds with humility and adoration:

46And Mary said: "My soul glorifies the Lord 47and my spirit rejoices in God my Savior, 48for he has been mindful of the humble state of his servant. From now on all generations will call me blessed, 49for the Mighty One has done great things for me— holy is his name. 50His mercy extends to those who fear him, from generation to generation. 51He has performed mighty deeds with his arm; he has scattered those who are proud in their inmost thoughts. 52He has brought down rulers from their thrones but has lifted up the humble. 53He has filled the hungry with good things but has sent the rich away empty. 54He has helped his servant Israel, remembering to be merciful 55to Abraham and his descendants forever, even as he said to our fathers."

desire and rule

Genesis 3:16 "to the woman He said, 'I will greatly increase your suffering and your childbearing; in pain shall you bear children. Yet your craving/desire(teshuka) shall be for your husband, and he shall rule(mashal) over you.'"

Genesis 4:7 "Surely if you improve yourself, you will be forgiven. But if you do not improve yourself, sin rests at the door. Its desire(teshuka) is towards you, yet you can conquer(mashal) it.

there is a clear connection between these verses. the dynamics in the relationship between Adam and Eve under the new fallen order are somehow equivalent to the relationship between sin and Cain.

A desires B. B will/can rule over A.

Eve and sin are A. Adam and Cain are B

Is Eve somehow equivelant to Sin? Is the Torah misogynistic? Or is there a different understanding of sin(chatat) in this passage?