In 1 Corinthians 11:2-16, Paul says:
2 Now I praise you, brethren, that in all things you are mindful of me and keep my ordinances as I have delivered them to you. 3 But I would have you know that the head of every man is Christ: and the head of the woman is the man: and the head of Christ is God. 4 Every man praying or prophesying with his head covered disgraces his head. 5 But every woman praying or prophesying with her head not covered disgraces her head: for it is all one as if she were shaven. 6 For if a woman be not covered, let her be shorn. But if it be a shame to a woman to be shorn or made bald, let her cover her head. 7 The man indeed ought not to cover his head: because he is the image and glory of God. But the woman is the glory of the man. 8 For the man is not of the woman: but the woman of the man. 9 For the man was not created for the woman: but the woman for the man. 10 Therefore ought the woman to have a power over her head, because of the angels. 11 But yet neither is the man without the woman, nor the woman without the man, in the Lord. 12 For as the woman is of the man, so also is the man by the woman: but all things of God. 13 You yourselves judge. Does it become a woman to pray unto God uncovered? 14 Does not even nature itself teach you that a man indeed, if he nourish his hair, it is a shame unto him? 15 But if a woman nourish her hair, it is a glory to her; for her hair is given to her for a covering. 16 But if any man seem to be contentious, we have no such custom, nor the Church of God.
The 1917 Code of Canon Law #1262 said:
§1. It is desirable that, consistent with ancient discipline, women be separated from men in church.
§2. Men, in a church or outside a church, while they are assisting at sacred rites, shall be bare-headed, unless the approved mores of the people or peculiar circumstances of things determine otherwise; women, however, shall have a covered head and be modestly dressed, especially when they approach the table of the Lord.
From Catholic Answers, Apologist Peggy Frye says, “[T]he document Inter Insigniores by the Congregation for the Doctrine of the Faith (October 15, 1976) stated that the 1917 Code of Canon Law (Canon 1262.2) requiring women to wear a veil on their head was a custom of the period, and that such ordinances, “probably inspired by the customs of the period, concern scarcely more than disciplinary practices of minor importance”, thus the “obligation imposed upon women to wear a veil on their head (1 Cor 11:2-16) no longer has a normative value." However, as a sign of respect, women should wear a veil when meeting the pope.”
Showing the Pope respect by covering your head when meeting him, but not showing Christ that same respect at mass does not sit well with me. I admit I do not fully understand the custom to cover your head when meeting the Pope. Nevertheless, I do feel that if it truly is a sign of respect, then we must give Christ that same respect, especially during the Eucharist.
I understand, and would like to mention, that this is a personal devotion for me. It is not binding in conscience upon anyone else. However, if after reading this and researching the Church laws, customs, and scripture on your own, you feel called to cover, go with your heart. Do not let the words of others sway you to believe that head covering is outdated and/or suppressive to women.