Versus 9 and 10 in that chapter are key to the answer... For the woman’s submission and because of the Angels.
Well, here is how I see it:
St. Paul adds this is why a woman, or wife, should have authority on her head when praying or prophesying in a public church service.
Some Biblical Scholars read this to mean that a woman should have a symbol of her husband’s or father’s authority over her. Others understand it to mean that woman should use her own “authority over herself” or self-control to cover her glory—her head, in this case—while in public.
In either case, women should cover their glory while praying or prophesying in a church service because of the angels.
That statement from Paul leads to suggestions from Bible scholars that range far and wide. Most conclude that Paul means angels observe our public worship services. Since they are watching, it is important for women to be appropriate in covering their glory and not dishonoring their husbands.
It bears repeating that most interpreters believe the specific issue of a woman covering her head to preserve her glory for her husband was related to the social standards of the time. Paul is relaying specific application of a universal principle: modesty. Christians may live in widely varied cultures, with variant standards of dress and fashion. All believers should appropriately “cover their glory” in public worship services according to conscience and the standards for modesty in their own era.