Thank you for your question! To start, I think you are correct in that St. Paul’s teaching was related to the culture at that time. The Congregation for the Doctrine of the Faith issued a declaration in 1976 called Inter Insigniores, in which they state about the teachings of St. Paul regarding women,
“. . .it must be noted that these ordinances, probably inspired by the customs of the period, concern scarcely more than disciplinary practices of minor importance, such as the obligation imposed upon women to wear a veil on their head (1 Cor 11:2-16); such requirements no longer have a normative value.”
Since the 1970s, women are not expected to wear head coverings while in church (though the expectation remains for Mass in the Extraordinary Form), leaving it up to a woman’s personal choice. As it is a choice, I can only share why I choose to do so. There are variety of reasons, but they are all part of a desire to recognize my femininity before God by wearing a veil in the presence of the Blessed Sacrament.
One such reason is that, when I put on my veil upon entering a church, it is a concrete reminder that I am in the presence of God. This fosters a disposition that helps me pray and focus (helpful for someone who is as easily distracted as I am).
I also wear a veil as a sign of submission to the will of God; however, for me, this is far more of an accountability measure than it is a sign of holiness. I continually struggle with surrendering my will to God’s, and wearing a veil helps me remember that I still have much growing to do in this area.
Finally, the veil reminds me that it is a great blessing to be a woman, as our bodies are sacred vessels capable of carrying life (think of how the chalice which holds the Precious Blood is veiled before the consecration). This is one attribute that distinguishes us from men. As a woman, I have a special vocation to receive life and nourish it, whether that be through loving my friends, in my work with college students, or one day as a mother. All of that being said, the veil is certainly not necessary for women to focus at Mass, surrender their will to God’s, or embrace the gift of their femininity. There are plenty of holy women in my life who inspire me and happen to not wear veils. In the end, I wear a veil because I like wearing one for the reasons I mentioned, and I hope that any woman would feel free to wear one or not, as she chooses.