Well, here's my personal beliefs of chapter 11.
St. Paul starts with two amazing verses:
"Imitate me, just as I also imitate Christ." and "Now I praise you, brethren, that you remember me in all things and keep the traditions just as I delivered them to you."
I think when St. Paul pleads with us to imitate him, the icon of Christ, and to not stray from the traditions he teaches us, then it seems very weak to attribute mere societal pressures to St. Paul. In fact, within the Orthodox Church, there is continued societal pressure to keep it the way it is.
One important question that ozgeorge asked is "Who in their right mind would want to become priest?" I'm a firm believer that priests who were called against their own will serve as better priests than those who wanted to be priests in the first place (this doesn't mean the latter was not called). So once you start having females protesting against the Church in wanting to be priests, then you have an issue. Male or female, those who want to be priests, I have issues with. It is the Church that chooses, and Christ that calls.
So moving on:
But I want you to know that the head of every man is Christ, the head of woman is man, and the head of Christ is God.
Here, St. Paul begins with a theological reason. The "shame" or "dishonor" that comes later is applied to both the male for covering his head, and female for not covering her head. And notice, both praying or prophecying must do this to remember verse 3.
Also, St. Paul does not end it at woman, but continues with Christ, saying that the head of Christ is God. Was it not the same St. John Chrysostom who said that that marriage of woman to man along with her submission is like the unity and submission of Christ to the Father? Therefore, St. Paul leaves us open with the fact that although woman is subject to man as the glory of man, yet both woman and man are of the same equal glory, just as Christ and the Father. If there be any societal pressures, this last part of verse 3 should not have been included.
Therefore, later when reading about what is shameful, or to be shorn or shaven, it must be read in a theological context as St. Paul started. Yes, it has turned into cultural, and may have been worse in Western circles where woman were brutally considered as second-class citizens, without clear Bible verses written by St. Paul himself, like verse 3 or the famous Gal. 3:28.
It is just as shameful by the way, for both man and woman in the Church to get closer to the Eucharist with their shoes on in the OO churches. "Shameful" may mean something societal, but there is also something theological, and seeing that St. Paul starts with a theological statement, his purpose is for spirituality.
So in parts where man is considered the image and glory of God, while woman the image and glory of man, then we can look at verse three and say that Christ is the image and glory of God. Does that mean Christ is not consubstantial to God? Away with such a thought! For as long as St. Paul starts with verse 3, and not because society frowns upon it, then "it is not so difficult after all to interpreting it other than a cultural context."
And even you agree that St. Paul clarifies this so that he doesn't put woman below man anthropologically:
Nevertheless, neither is man independent of woman, nor woman independent of man, in the Lord. For as woman came from man, even so man also comes through woman; but all things are from God.
Indeed. He tells us we need one another, and that no one is above another, but all things from God. The preservation of this verse, and the likes of verse three makes the idea of women as second-class citizens not only wrong, but a heresy, in my opinion.
Judge among yourselves. Is it proper for a woman to pray to God with her head uncovered? Does not even nature itself teach you that if a man has long hair, it is a dishonor to him? But if a woman has long hair, it is a glory to her; for her hair is given to her for a covering.
To read this, it seems to make sense. Not only is he reiterating the same words "dishonor" and "glory" that can be seen in a theological light, not necessarily a cultural light, but even in cultural ways, this statement still holds true for today, even there's a select vociferous few.
I like to see woman always with reasonably long hair, and longer would be nice, but men usually do not have long hair, and it is considered a dishonor. Now, the length of the hair is to every culture's judgment, but I would say that a man who extends his hair to his shoulders is pushing it. I may sound stereotypical, but you don't see lots of men with very long hair, or women with very short hair. Thus, my stereotype stands because the culture around me makes me think this way.
It's interesting, since culture still holds somewhat what St. Paul holds in this verse, then we continue to see St. Paul's point, who started with a plea not to change the traditions, and ends with a command not to be contentious:
But if anyone seems to be contentious, we have no such custom, nor do the churches of God.
I can't help but wonder. Why did he include this last verse? Were there indeed those rebellious ones in the Church who wanted to change tradition or custom?
Backtracking a little:
For this reason the woman ought to have a symbol of authority on her head, because of the angels.
This is one verse I don't understand. Why "because of the angels?" What do angels have to do with head coverings? Are women like the Cherubim who cover themselves before the Lord?
I would not say that our Lord succumbed to societal pressures, but rather that he chose for his ministry those who would be most effective and in the misogynistic society of the day the most effective people happened to be men.
But then this begs the question why the Lord still allowed "misogynistic" societies to flourish under the guidance of His chosen men. I don't think the same Lord who claimed Himself Christ and was crucified while society was looking for a warrior Christ would have had the same pressures to choose men only for priests.