When considering the relationship between men and women, both in the family and in the church, I believe the central issues revolve around authority. Conflicts are very often conflicts of authority. The origin can be traced to Satan himself when he said, "I will no longer be under the authority of God. Instead I will rise up and be like the Most High" (see Isaiah 14:12-15). From then until now, Satan has been at war with God, seeking to turn all he can against God and His authority in their lives.
Paul expresses God's flow of authority as follows: "But I want you to know that the head of every man is Christ, the head of woman is man, and the head of Christ is God" (1 Cor. 11:3). Paul goes on to make application of this truth about men and women, but for now I want to focus on that one statement. First, notice that it does not relate to who is more important. Paul says, "God is the head of Christ." We do not think less of Christ because He took His appointed place under God. All through His earthly ministry, Jesus submitted Himself to His Father. He said He did not do His own will, but submitted Himself to do the will of His Father. We do not think Christ to be inferior because He did that, but rather we think more highly of Him! (See Philippians 2:5-11.)
When Paul says that man is the head of woman, it is in the same light. Woman is not of less importance or worth; this is simply a statement of God's creation design for man and woman, and He has fitted both perfectly for this relationship. All He asks is that men and women accept their God-given roles, then function in their roles by faith. God's promise is to bless them if they will. And just as Christ was lifted up and given a name above every other name, woman will also be lifted up and partake of the blessings and glory of God as she accepts her place in God's plan.
Satan came to Christ to tempt Him to exalt Himself in miraculous ways (see Luke 4:1-13). But Christ refused the offer of the enemy and chose to go God's way, which was Calvary (Phil. 2:5-11). It was not an easy way, but it was God's chosen will for Him. Likewise, the enemy came to Eve to draw her away from what God had commanded. She believed the lie of Satan and was deceived. She then became the instrument of Satan to pull Adam down with her. Paul says that Eve was deceived, but Adam was not. He knew what he was doing; thus, God held him accountable for leading the whole human race into sin.