Your question is a very good one an deserves an honest theological answer. The truth of the matter is that the covering of the head did not begin as a religious practice among Christians. It was a carry-over from Judaism. The Gentiles never did it. As the Roman Empire collapsed and the world evolved into the Middle Ages, it became very common for women to cover their hair.
It had two purposes. One was the people in those days (Middle Ages) did not shampoo their hair everyday. To keep it clean they covered it. The second thing that happened was that the headcoverings became more elaborate with social strata. The aristocracy wore very fancy head covering, except for the queen and the princesses.
When women attended mass, the aristocracy sat up front. They wore very regal clothing, with head dresses. The poor stood in the back and they usually wore very simple clothing such as cloaks and hoods or simple veils very similar to what nuns used to wear.
As you can see, it was never about Christ. This was introduced long after veils came into use. As veils fell out of disuse the Church tried to teach women against the sins of vanity and used a very common method, the head covering. I say common, not to mean vulgar, but common to many cultures. A woman’s hair was her glory. So in many cultures women covered their hair. That’s why our own sisters and nuns covered their hair, Muslims too, Hindus, and Jews. That’s how the veil took on a religious meaning.
In the 20th centiury very few people thought of a woman’s hair as her glory. Maybe because you could see more. Women wore short skits, short sleeves, lower cut tops, pants, shorts, etc. Women also washed their hair. Therefore the two original reasons for covering their hair were no longer needed. Keeping it clean is much easier today than it was. Modesty is not about covering the hair. Women need to cover their bodies more than their hair.
The reason that women cover their hair to meet privately with the pope is because popes command it. As Catholics we bow to their wishes. But what is interesting is that Catholics are not the only ones who bow to their wishes, all Christins do, including Protestants. There are three groups of women that the papacy allows to enter into private meetings without a head covering: Hindus, Jews, and queens. It would be disrespectful to them. Though Catholic queens often do wear a black veil.
And yes, it was a beautiful mass and I want to see the videos, because I tuned out early. I had to go somewhere. I only saw up the consecration. I’m sure that there were closing remarks.
Fraternally,
Br. JR, OSF