That chapter in 1 Corinthians is symbolic, and the “man” and “woman” he talks about in that passage should be understood as the soul and the body, respectively.
Evagrios the Solitary explains this in his text “On Prayer”:
If a man, still enmeshed in sin and anger, dares shamelessly to reach out for knowledge of divine things, or even to embark upon immaterial prayer, he deserves the rebuke given by the Apostle; for it is dangerous for him to pray with head bare and uncovered. Such a soul, he says, ought ‘to have a veil on her head because of the angels’ who are present (cf. 1 Cor. 11:5-7), and to be clothed in due reverence and humility. (Text 145)
Let’s take a moment to analyze that. Evagrios is saying that a
man should not pray with his head bare, and he equates that to St. Paul who specifically says that men should pray with their heads bare (1 Cor 11:4) and women should pray with their heads covered (1 Cor 11:5).
So in the text, Evagrios’s usage of the word “man” is physical; it means “any person.” St. Paul’s usage of the terms is symbolic, and St. Paul explains the symbols, just in case we’re having a hard time:
A man… is the image and glory of God [spiritual], but woman is the glory of man [physical]. – 1 Cor 11:7
So in the context of that passage, “man” represents the spiritual side of each one of us, and “woman” represents the physical side. This is because the physical body, whether male or female, is always receptive (or feminine) because it receives the influences from the spiritual world. The “driver” of the physical body is the soul, therefore it is (symbolically) masculine, or projective, because it is projecting its influence into the receptive (symbolically feminine) physical body.
So by saying women must cover their heads when they pray, Paul is saying that we must all (male and female) cover
our physical nature. That is, don’t go to God praying about petty material things. But approach God with spiritual things (that is, have your spiritual side uncovered).
The statements about hair length that you are mentioning are given in the context of those earlier statements about the head coverings. Paul is pointing out that the culture has a custom that reflects this symbolic truth about how we should approach God, and we should learn a spiritual truth from that custom.
It has nothing to do with whether you are physically male or female, and nothing to do with physical head coverings or hair length. This is a passage about prayer and the way that we approach God.