No, he is actually quite clear in the bible: women should be covered when praying. He leaves no doubt who is who in this world (1 Cor 11:3)
But I want you to understand that Christ is the head of every man, and the man is the head of a woman, and God is the head of Christ.
No extra-Biblical knowledge required here.
Brothers, Jesus did not die so that women could remain subservient or inferior to men any more than He died so that kings could rule or slaves could remain faithful in their service to their masters
Actually, Paul thinks otherwise (1 Cor 11:7)
For a man ought not to have his head covered, since he is the image and glory of God; but the woman is the glory of man
He is my covering.
That's not what the Bible says.
So, do we have a conflict here between what you say Christ did and what Paul teaches?
Look, if you are seeking a gender-neutral faith, good luck. But you can't make Christianity something it never was gender-neutral.
Either the Bible is a God-inspired revelation or it is a man-made delusion. There is no middle. It is not mutable. It's not subject to fads and cultural clichés.
Gen 3 vs. Gen 1 is a theme that seems to confuse the metaphor-challenged atheist and it seems that these two versions of the Creation are challenging you, too.
Gen 1:27,28 So God created man in his own image, in the image of God he created him; male and female he created them. And God blessed them. And God said to them, “Be fruitful and multiply and fill the earth and subdue it and have dominion over the fish of the sea and over the birds of the heavens and over every living thing that moves on the earth.”
Mat 19:4-9 He answered, “Have you not read that he who created them from the beginning made them male and female, and said, ‘Therefore a man shall leave his father and his mother and hold fast to his wife, and they shall become one flesh’? So they are no longer two but one flesh. What therefore God has joined together, let not man separate.”
They said to him, “Why then did Moses command one to give a certificate of divorce and to send her away?”
He said to them, “Because of your hardness of heart Moses allowed you to divorce your wives, but from the beginning it was not so. And I say to you: whoever divorces his wife, except for sexual immorality, and marries another, commits adultery.”
Every human is created in the image of God. Am I not God’s temple and doesn’t He dwell in me as He does in my husband? I know Whom I trust for my reconciliation to the Lord, I know Who circumcised me, Who covers me, in Whom I have life rather than death, Whose Spirit dwells next to mine, Who is the “Head of all rule and authority” to me long before I became my husband’s wife.
And we know that Corinthians 11 is unique because it opens by speaking of traditions:
1Co 11:1 Be imitators of me, as I am of Christ.
1Co 11:2 Now I commend you because you remember me in everything and maintain the traditions even as I delivered them to you.
1Co 11:3 But I want you to understand that the head of every man is Christ, the head of a wife is her husband, and the head of Christ is God.
We understand that we don’t really understand what Paul meant when he said that a woman should have power over her own head for the sake of the angels. We should understand that Jesus prayed in the Temple, that he most likely used a prayer shawl, and it was not a shame for Him.
However, those of us who have looked into the original as best as we can, understand the depth of the meanings of the words kephale, “head” and doxa, “glory.” We should go out in front, and reflect the image of God in worship and submission to one another. We certainly believe that the whole is of God.
Because we also know Christ’s teaching about submission: loving and willing submission doesn’t make anyone “subordinate,” that we should submit one to another, and try to make ourselves the least, not the greatest. Christ showed He was one with the Father in submitting to His will. We are one in the One, different members in the body “holding fast to the Head, from whom the whole body, nourished and knit together through its joints and ligaments, grows with a growth that is from God.”
BTW, you haven’t explained whether women with alopecia from disease or chemotherapy are shamed by being bald, and can’t pray.