“Adam exercised leadership in naming Eve”?? There is nothing in the text to suggest this. Nor does the text say that God named man. The Genesis record refers to him as “Adam” due to his origin: he was made from the dirt. “Adam” means “dirt”. The reason Adam names Eve is because of her origin. He knows himself as “ish” (Hebrew) and he names his companion “ishaha” because he recognizes her to be the same as him, yet different. God’s intent in creating Eve was for her to be a “suitable helper”, not a servant. The Hebrew term for “suitable helper” (ezer kenegdo) in no way indicates a lower rank or subservience or submission of any kind. It means they were two parts of the same whole, two sides of the same coin. The narrative further cements this equality by saying that both were created in God’s image. Nowhere does God put Adam in authority over Eve nor does He put Eve in subjection to Adam. In fact, OT writings show Israel referring to God as her “ezer” and we never think of rendering that as a lesser or subservient or submissive role for Yahweh. Adam’s exercise of authority over Eve was a direct result of sin as his own selfish nature was given vent and he sought power over his mate. Likewise, Eve sought dominance (“your desire will be for him”) and the subsequent cultural trend would show that males, by and large, won this sinful struggle. Further, Nowhere in the law or the rest of the Old Testament does God place men in spiritual or civil authority over women nor does He instruct women to subject themselves to that patriarchy. God chooses to operate within that existing paradigm and embeds legal protections for women within His laws for Israel. The only legitimate appeal to Genesis 2 is for the one-flesh union and the equality of women and men.
What did Adam do prior to naming Eve? He named the animals, they were brought before him to name. This naming is an act of being over them, thus he names Eve at the very end. You say "Adam’s exercise of authority over Eve was a direct result of sin as his own selfish nature was given vent and he sought power over his mate." there is a reason though that humanity was under the sin of Adam and not the sin of Eve, because he abdicated his responsibility for her, and she fell into deception. So we are under the sin of Adam not Eve because he had headship so it ultimately falls on him. I agree on your understanding of this "ezer" term not being inherently indicative of headship, in this case Eve was brought along his task of taking dominion, which he already had started. Whereas Israel did not start their mission then God tagged along. God assigned the mission created the people and helped them. So it does not work as a direct parallel. Paul later refers to all this that he does not allow a woman to exercise authority over a man, then refers to her falling to deception. 1 Tim 2:12-14 The Ephesians text as well is quite difficult to argue around given that Paul ties in the position of men and women, and relates that to a theological truth of Christ and the church (Eph. 5:25-33). So this relation between man and woman are actually analogical to a cosmic truth. So I think what the text forces us to do is to expand our views of this relationship, not get tied to this subordination language. It is actually about liberating one another to express God's intent for both man and woman, which are different, and in doing this we actually destroy the work of the fall, and this tension between the sexes. We have to use Biblical categories and definitions rather than secular understandings of these terms and ideas. Equality does not equal same.
