It is for this reason that a woman ought to have authority over her own head, because of the angels. – 1 Corinthians 11:10
The passage in Corinthians clearly teaches of headship where God is the head of Christ and Christ is the head of man and man is the head of woman. Though Biblical submission is right woman are not inferior spiritually but one in Christ. Yet they must choose to submit and humble themselves just as Christ humbled himself before the Father. God’s government and way of order is in such a way where each member must do his or her part. When women or men choose not to fulfill and walk in God’s ways for the Church, disorder and every evil practice ensues. The importance of head covering is not an outward reason but an spiritual reality proclaimed to the principalities and powers. When the head covering is practiced it proclaims God’s order and way to all of creation, including the angels (1 Peter 1:12). K.P. Yohannan says, “Have you considered why there is so much tension and fighting over placing a small piece of cloth on one’s head? When a woman wears the symbol of God’s government, a head covering, she is essentially a rebuke to all the fallen angels. Her actions say to them, ‘You have rebelled against the Holy God, but I submit to Him and His headship. I choose not to follow your example of rebellion and pride.'” Eve fell into satan’s rebellion (2 Corinthians 11:3), yet now in the Church women declare they are following God’s order in the Church (1 Timothy 2:12-14).
Watchman Nee says, “When many of the sisters in the church take the place given to woman and learn to cover their heads, they send out an unspoken word of testimony to the angels in the air, to the effect that God has obtained in the church what He desires.” Hippolytus an early Church Father wrote, “let all the women have their heads covered.” Others who taught this practice in the Church were, John Calvin, Martin Luther, Early Church Fathers, John Wesley, Matthew Henry to name just a few. We must remind ourselves that until the twentieth century, virtually all Christian women wore head coverings. As we worship together as the Church we enter into worship with the holy angels in heaven who cover their faces (Isaiah 6:2). In the same way sisters covering their heads show they honouring of the glory of God. Clement of Rom in A.D. 96 said, “Then let us gather together in awareness of our concord” speaking of the holy angels when we worship. The Church is to gather and worship God in the spirit (John 4:24) doing things that the world considers foolish but for the Lord there is great significance. Paul speaking as inspired by the Holy Spirit said, “we have no other practice—nor do the churches of God” (1 Corinthians 11:16). It was not just a local custom or practice but all the Churches were practicing this as with water Baptism and Holy Communion. This was not an optional thing as the default was all the Churches were doing it. But Paul gives grace to those who are not convinced of its importance from the Lord as the Corinthians partly were divided over many issues including this one.