This question is easily answered in this clear, charitable and wonderful article by Rebecca DeVendra posted at OnePeterFive.com
In my experience, it is impossible to talk about the Catholic custom of womenwearing chapel veils at Mass without encountering judgment. Progressives will insist that the practice is an outdated custom to be tossed aside. Reactionaries will declare that women who do not cover their heads in Mass are sinning and that canon 1262 is still in force.
Both are wrong.
Here is what we all need to realize about the chapel veil: it is a form of devotion to God that is only open to a woman. This means that it is a strictly feminine form of prayer that excludes men. Men who cover their heads during Mass signify a rejection of Christ; it is to dishonor His spiritual head. Even a priest who wears his biretta will remove it when in prayer: he never wears it while kneeling or while standing at the altar reciting the prayers of the Mass. Women, however, may veil at all times when in the presence of the Lord because they have a sacred role that demands their dignity be acknowledged.
Catholic people who do not understand the custom of veiling and push against it usually do not realize their own inconsistencies. Would they say, for instance, that nuns ought not to wear habits? That a bride ought not to wear a veil on her wedding day? That a young girl receiving Communion for the first time ought not to be veiled? The veil or desired head covering in these instances is never a symbol of oppression. It would be ridiculous to apply most arguments against the chapel veil to these instances:
“Yuck, you’re wearing a veil on your wedding day? You look so silly. You do know you’re not a Muslim woman, right?”
“Why is that nun in a habit? Does she think she’s better than me?”
“Why are you wearing that thing on your head for your first communion? Is some man making you do that? You poor thing.”
I have encountered comments just like the ones above for veiling. I veiled for the first time as a teenager, and I was made so self- conscious by the critiques I received that I stopped doing it. It was as if I called everyone’s attention to my motives, and was suspect. I eventually reasoned to myself that since the chapel veil was also a sign of virtues like chastity or modesty, that I was only calling attention to myself for being one of the only parishioners wearing one. Therefore, since the goal was not to be a spectacle, I could conform to the customs of the parish and not wear one. It’s not a sin after all. Cardinal Raymond Burke, while he held the office as Prefect of the Apostolic Signatura, stated this:
The wearing of a chapel veil for women is not required when women assist at the Holy Mass according to the Ordinary Form of the Roman Rite. It is, however, the expectation that women who assist at the Mass according to the Extraordinary Form cover their heads…It is not, however, a sin to participate in the Holy Mass according to the Extraordinary Form without a veil.
Burke strikes a subtle balance here. The Church, in her traditional liturgical practice, adorns things that are sacred. We veil our altars, decorate our tabernacles with gold and jewels, and robe our priests in beautiful vestments to signify the dignity of their office. It is certainly not sinful to do away with these things, but the outward acknowledgement of the dignity due to them is laudable and conducive to humility. As St. John Chrysostom said, “Christ appears when the Priest disappears.”
Paul states in I Corinthians 11:10-12: “That is why a woman ought to have a veil on her head, because of the angels. Nevertheless, in the Lord woman is not independent of man nor man of woman; for as woman was made from man, so man is now born of woman. And all things are from God.” (RSV)
I’d like to offer some historical context to this verse. The word “veil” in the English translation above is from the Greek word exousia (ἐξουσία) or “authority.” It would be an acceptable translation to say in English, “A woman ought to have authorityupon her head.” Further ancient usage of the word puts exousia in the context of might or power, or even an office like magistracy. To interpret this use of the Greek word for “authority” to mean the authority a woman is subject to would be laughable to Greek scholars.
William Ramsey, late professor of Classical Archeology and New Testament Scholar explains:
Authority or power that belongs to the wearer, such power as the magistrate possesses in virtue of his office, was meant by the Greek word exousia. So Diodorus, i. 47, describes the statue of the mother of the Egyptian king Osymandyas, wearing [literally, “having”—bt] three royalties upon her head, i.e. she possessed the royal dignity in three different ways, as daughter, wife and mother of a king. The woman who has a veil on her head wears authority on her head: that is what the Greek text says.1
Paul knew how his audience would interpret the word exousia. He is not talking about the dignity of women in this passage because it is implied. He is affirming a woman’s right to pray. Men and women are equal insofar as both come from God, but we are not androgynous. With this understanding we can see that a Catholic woman has a special relationship with God, and her act of veiling in His presence is centered on her relationship with Him. Contrary to popular assertions, Catholic women are not commanded to cover their heads in the presence of men, like the Islamic practice of the hijab which requires women to cover themselves from head to toe in order to ward off lustful men. The chapel veil is an affirmation of the woman’s dignity in the presence of the Lord, and of her right to pray alongside men.
I wear a veil regularly now at Mass. It took some time and prayer to feel at home in it. It helps to find a parish where half of the women wear head coverings (veils or scarves or hats, as all of these things are acceptable substitutes), and to know that people will not make it their personal mission to comment on your attire. I can assert comfortably now that there is great solace in the practice of veiling. It is conducive to prayer, and like all acts of loving devotion, freely chosen.
Modesty, chastity, dignity. This is what a chapel veil represents, and it belongs to a woman in respect to God, not only to man. It is a symbol of her authority and of her right to communicate with God in a specifically feminine form of devotion.
Really, who are you to judge?