The bible tells us that the man is the "image and glory of God" (1Cor. 11:7). Any covering on the man would veil God's glory in the church. In order for God's glory to be seen alone in the church, the men remain uncovered by not having long hair, and by removing any head coverings.
The women are the stewards of the coverings. There are two competing glories in the church- 1. "The woman is the glory of the man" (1 Cor. 11:7). 2. And "if a woman have long hair, it is a glory to her" (1 Cor 11:15). Because there are two symbolic glories to be covered, there are two coverings. First covering is the woman's long hair (v. 15b) to hide the glory of the man (the woman herself). The second covering is to hide her own glory - her hair.
This way God's authority is declared in the church. Symbolically, man's glory is veiled, while God's glory is seen. Men in their ministry are reminded that their glory is to be hidden. The bible tells us that even the angels are instructed by it. (1 Cor 11:10).
Did you memorize any scriptures about that?
/johnny