Taken from this article by Bill Einwechter from Vision Forum Ministries:
The scriptural revelation of the creation of man and woman, and the scriptural commentary on their creation establishes the headship of the man over the woman. The text of Genesis 2:7 and 2:18-24 teaches us that man was made first, and then the woman was made to be man’s helper and companion. The Bible instructs us that this order of creation was by God’s design, and that it establishes the positional priority of the man over the woman in regards to authority and leadership. In setting forth the authority of the man over the woman in the context of the local church, Paul appeals to the creation order saying, “For Adam was formed first, then Eve” (1 Tim. 2:13). In another passage, Paul states the divinely ordained order of authority and headship: “But I would have you to know, that the head of every man is Christ; and the head of the woman is the man; and the head of Christ is God” (1 Cor. 11:3). Therefore, the Apostle Paul teaches that God has decreed that the order of authority be as follows: God-Christ-Man-Woman. Each one in this “chain of command” is under the headship (i.e., authority) of the one preceding him or her. Later on in this same text, Paul, as in 1 Timothy 2, calls upon the order of creation to show man’s headship over the woman. He says, “For the man is not of the woman; but the woman of the man. Neither was the man created for the woman; but the woman for the man” (1 Cor. 11:8-9). The Bible explicitly states that the man has headship over the woman, and that this headship is not based on cultural factors, or even the fall; rather, it is based on the created order established by God Himself.
Now it is also plain in the Bible that God has ordained that the order of the headship of man must be maintained in each governing institution set up by God. There are three primary institutions established by the Lord for the ordering of human affairs. These are the family, the church, and the state. Each of these institutions has authority to govern within its appointed sphere. We could say, then, that there are three “governments” in the world: family government, church government, and state government. In each of these governments, God has commanded that men bear rule. The man has headship in the family (Eph. 5:22-24), the church (1 Tim. 2:11-14; 1 Cor. 14:34-35), and also by implication and command, in the state as well (1 Cor. 11:3; Ex. 18:21; see point 2 below).
Could it be that the man has headship only in the family and the church but not in the state? No, this could not be, lest you make God the author of confusion, and have Him violate in the state the very order He established at creation and has revealed in Holy Scripture! If one is going to argue for the acceptability of women bearing rule in the civil sphere, then to be consistent, he or she also needs to argue for the acceptability of women bearing rule in the family and the church. Now it is true that some attempt to do just that; but their denial of male headship for the family, church, and state is really a rejection of the Word of God and is a repudiation of God’s created order. And it is not sufficient to contend that it is acceptable to support a woman for civil ruler when she is the best candidate, unless you are also prepared to argue that it is acceptable to advocate a woman for the office of elder because she is better suited than the available men in the church; and unless you are also prepared to say that the wife should rule over her husband if she is better equipped to lead than her husband is.