The reason for the statement in I Corinthians 11 regard angels is simple, really. When a woman leaves her hair uncut, her hair is a symbol of the covering of grace. The concept of covering, especially of the angels covering, comes from the OT. First of all, everything that God does has a purpose. When God told Moses to put two cherubims covering the mercy seat, that wasn't by accident. Those cherubims where physical images of the spiritual cherubims that covered the glory of God, a position that Lucifer held prior to his fall, as stated in Ezekiel 28:14. The mercy seat, where the mercy of God met with the judgement (Psalm 85:10) was the seat of the glory, and Lucifer was the angel tasked with covering. In the NT, when a woman leaves her hair uncut, she takes the place of the angels in covering the meeting place of the mercy of God and the judgement of God. In the OT, the blood of a spotless lamb was placed on a literal seat. In the NT, the blood of the Perfect Lamb is applied to the heart of a repentant sinner. But in both cases, the principle of covering rings true.