Meshvas Nefesh (Bereishis 3:16): And now it remains for me to explain the original thought of creation that man and women were created equal, on the same level and with two faces. Similarly we see that the sun and the moon go through the same window and the moon claimed that it wanted to go into another doman that it wasn’t fit for. Consequently the moon was reduced in size to be subordinate to the sun so that it can only shine when facing the sun. As our Sages note that the sun has never seen the diminishing of the moon because the part which appears to be diminishing is because it is not receiving the light of the sun. So also originally the male and female were created to work the Garden of Eden and to guard it. The job of working it was given to Adam and the guarding was given to Eve. Thus anything to do with the garden was Adam’s responsiblity and anything related to guarding it was Eve’s responsibility. Thus they were equal in level as two friends. And it is well known that two friends who have a close relationship and are equal in level – if they want to have a peaceful relationship it is necessary for each to nullify his own view for that of his fellow. Thus we see that Eve violated two aspects of their agreement. First of all she violated her responsibility to guard the Garden when she allowed the Serpent to enter it. Second not only did she not guard the Garden she also violated the Divine command not to eat from the Tree of Knowledge and furthermore she pressured her husband to also eat from it because if he resisted her request he was afraid that it would reduce the peace between them. And this is exactly how Adam defended himself against G-d’s accusations. He replied, The woman which You gave me... i.e., “who is equal to me” as I explained before. We see this from the fact that the gematria of “the woman” is the same as “man”. Furthermore Adam said “who You gave with me” i.e., she is equal to me and he didn’t says “who You gave to me”. In other words since You have given her to me to be my companion and that we are both equal in level, I listened to her and nullified my wishes before hers for the sake of peace. We know that G-d Himself allows His name to be erased for the sake of peace in the case of the Sotah. And because of this perception of Eve brought about destruction since she in fact thought she was equal to Adam - she was punished measure for measure that the man should rule over the woman. This is why the man acquires the woman in marriage as it says, “When a man acquires a woman” and it doesn’t say when a woman acquires a man. As is know that whoever acquires something is in control of the purchase. Similarly by divorce, the man is in full control as it says, “And he writes the documents of divorce...” and it doesn’t say that she writes a document of divorce for him.
Tzaror Hamor (Bereishis 3:12): And then Adam replied with an answer that was worse than the first. And he said, The woman which You gave to be with me. Adam was thus equating the slave to the master. Is this the reply of a wise person for whom the King decreed upon him not to eat something specific and he ate it and was now justifying his actions by saying that another slave commanded me to eat it?! Furthermore he is continuing his rebellion and his not showing any regret that he will no longer sin. Instead he is saying I am now eating it and not I ate it – but I am continuing to eat what is left. Therefore he received a double punishment. In contrast the woman replied honestly that the Serpent seduced me to sin because of my weak mind.
Rav S. R. Hirsch (Bereishis 3:12): The woman which You gave to be with me. You wanted that she be equal with me and You commanded that we are to form not only one heart and one soul but also “one flesh”. As one body to fulfill the spiritual desires and wants and that they should be united in will and deed. And this woman – she gave it to me to and her will was decisive for me. Notice that Adam is not claiming that his lust overcame him or that the woman had led him astray. His defense was very simple that he did what his wife wanted.; So here is revealed the equality and harmony which was originally supposed to be between man and his wife.