The egalitarians sometimes say that the judgment of God upon Eve--where God says "your desire shall be for your husband and he will rule over you," (Gen. 3:16)--is not part of God's perfect plan. Instead, it is a result of the fall. They then say that since Christians are not under condemnation and having to keep Old Testament Law, then the curse upon Eve is no longer valid and does not apply to women today.
In the article, Genesis 2, Adam and Eve, and Authority, I established that before the fall, Adam named the animals. Eve did not. Naming them was his first act of dominion, and it is a sign of authority. Also, Adam named Eve (Gen. 2:22-23, 3:20) and exercised his authority over her--before The Fall.
If the curse of God is no longer valid, then what about the rest of that same verse that says that a woman will have pain in childbirth? "To the woman He said, “I will greatly multiply Your pain in childbirth, In pain you shall bring forth children; Yet your desire shall be for your husband, And he shall rule over you,” (Gen. 3:16). Obviously women still have pain in childbirth, so, apparently, the curse is still valid.
Paul taught that women are to be under authority, and he relates it to the created order. 1 Cor. 11:7-10, "For a man ought not to have his head covered, since he is the image and glory of God; but the woman is the glory of man. 8 For man does not originate from woman but woman from man; 9 for indeed man was not created for the woman’s sake but woman for the man’s sake. 10 Therefore the woman ought to have a symbol of authority on her head."
So, we can see that the argument that Adam ruling over Eve is not God's perfect will and that it is not for Christians today does not stand in the light of Scripture. Therefore, the egalitarians objection is invalid.