Should women wear veils during worship?

According to the Lectionary, I should be reading chapter 12 of the first epistle to the Corinthians. However, I don't want to miss anything and so, I read chapter 11 instead. This is not an easy chapter to understand. No wonder, it is not included in the daily reading texts.
Paul began by appealing the Corinthians to imitate him. He was very good at writing one-liners. This one is a top-quality aphorism.
Be imitators of me, as I am of Christ (1 Corinthians 11:1).
Matthew had a hard time with the Scribes and Pharisees. He recorded the following warning from Jesus.
The scribes and the Pharisees sit on Moses' seat;
so practice and observe whatever they tell you, but not what they do; for they preach, but do not practice (Matthew 23:2-3).
St. Paul was a reformed Pharisee. He was different from his fellow party members. So, he could encourage the Corinthians to imitate him. As a teacher, I myself dare not tell my students to imitate me. I do not always practise what I preach. I am fully aware of my pride, arrogance and weaknesses. Therefore, I do not have the moral authority to tell my students to follow my behaviours. How can I tell my students not to smoke when I myself smoke a pipe in my nocturnal reading? St. Paul is admirable indeed. He preached what he practised.
Then Paul began to touch on the issue of women wearing veils during worship. I think this issue was culturally determined. Its teachings might not be applicable elsewhere. This position of mine may raise the eye-brows of some of my readers who think that the writing of the Bible is inspired by God. Therefore, the Bible contains nothing but the truth. To say that the truth recorded in the Bible cannot be applied elsewhere will infuriate many people.
In patriarchal societies, women are deprived of the opportunity to exercise authority. So, when a lady became the Supreme Ruler of Mainland China, many people would be unhappy. Some felt that a lady emperor was "a female rooster summoning the dawn." Of course, the patriarchal societies were wrong. Just survey the leaders of the world and you will find lady presidents, Queens and ministers etc. So, how are we to handle the problem of forcing women to wear veils in worship?
For a man ought not to cover his head, since he is the image and glory of God; but woman is the glory of man.
That is why a woman ought to have a veil on her head, because of the angels (1 Corinthians 11:7, 10).
The logic does not follow. Man should not cover his head because he is the image and glory of God. Now, woman is the glory of man. Then why should she cover her head. Put it in another way, if the glory of man should cover her head, shouldn't the glory of God cover his head even more?
Then St. Paul argued from the natural world.
Does not nature itself teach you that for a man to wear long hair is degrading to him,
but if a woman has long hair, it is her pride? (1 Corinthians 11:14-15)
Then all the male in China in ancient times were degraded! Therefore, my only conclusion is that women wearing veils in worship is only a culturally determined practice not necessarily applicable to worships in other parts of the world.
Chapter 11 also gives us Paul's theology of the Holy Eucharist (1 Corinthians 11:23-27). It also tries to tackle the manner with which the Corinthians handled the Lord's Supper. Much background information about how the Agape was conducted in Church is not available. Scholars have to conjure up some educated guesses as to what had actually happened. We are able to identify some issues: factionalism (11:18-19), lack of charity (11:22) and did not receive the body of the Lord in worthy manners (11:27-30). There are quite a number of real issues to handle. Unlike the practice of veiling the head, these issues are universally applicable.

My dear Advocate, You inspired culturally conditioned authors to write the Bible. The spirit is more important than the letters. Empower us to be able to discern the message You want them to convey to us. Amen.