This is what I came up with when I looked into it. Please understand this is my take on it. I am not claiming that I have fully studied it enough to have a definite conclusion
This practice is a symbol. What this symbol represents is something that all women should have a proper heart attitude about. The headship of husbands and fathers. We know from other passages that a wife should be submitting to and reverencing her husband.
Feminism
From the research that I have done it seems like this was a typical practice for most Christian women up until the early to mid 20th century. One thing that I have definitely not found is this practice being spoken against until recent years. I believe that when feminism began to infect churches this symbol of submission was rejected because women considered themselves as equals to men in every way. I obviously cannot prove that feminism was the cause of this going away but I do believe the mindset of feminism has infiltrated churches in many ways that we don't even realize.
When is this necessary?
From the context of the passage I believe this applies to corporate worship (v2, v16, v18) within the church and not necessarily to all times of prayer. This is a distinction that I believe is misunderstood by some denominations such as Mennonites and Amish who practice this at all times. From the passage I believe that it is necessary any time a woman is teaching or anytime she is praying or in attendance during public prayer. (she should be joining in prayer anytime she is in attendance and someone is praying publicly)
Headship
Verses 3, 8 & 9 teach the authority structure from creation. These are the facts of creation that are symbolized by the head covering. “The head of every man is Christ: and the head of the woman is the man; and the head of Christ is God.”
I believe there is nothing here teaching that the woman is of lesser value. The statement “the head of Christ is God” stands directly beside “the head of the woman is the man.” We know that Christ is valuable to God—He is God. The issue is order and authority structure. Not value.
In Ephesians 5, the headship of Christ is spoken of as it relates to the Church as his bride. In 1 Corinthians 11, His headship in the assembly is related individually to the believer within the context of corporate worship. In verse 4, the covered head of the praying or prophesying man is dishonoring to his head which is Christ (v3). This is why Christian men remove their hats when they pray and even non christian men commonly practice this still today in society.
Verse 5 teaches that a woman’s uncovered head dishonors her head which is the man. The word dishonor means, “to shame down or disgrace.” When a man appears with his head covered, or a woman with her head uncovered, it is a denial of the teaching regarding headship.
Glory
Paul also teaches us about glory, which is another reason for us to follow this practice.
The reason for the uncovered head of the man is given: “Forasmuch as he is the image and glory of God.” Man must not, cover his head in the assembly because he represents God as His image. Also, he is the glory of God. God’s image and glory must not be hidden. These are two reasons for the uncovered head of the man.
The woman is not spoken of as the image of man, but she is spoken of as the glory of the man. The glory of man must not be manifest in corporate worship, therefore that glory must be covered. No glory but God’s is to be displayed while worshiping God. Mans public ministry is to be done so that God alone receives the glory.
Some will cite verse 15, “Her hair is given her for a covering.” Since she has hair or long hair, they say, that is enough. Notice that for the woman there are two glories involved. She is a glory: “The woman is the glory of the man” (v. 7). But she also has a glory of her own. Her hair is a glory to her (v.15). For the glory that she is (the glory of the man), God has given her a natural covering, (her hair). For the glory that she has (her hair), she must submit her will and cover that with another covering which she places over her own glory.
By covering “the glory of man” (the woman) and covering the woman's glory (her hair) and leaving uncovered “the glory of God” (the man), we are allowing God alone to receive the glory.
To argue, then, that long hair is the woman’s head covering seems to miss the very point of the function of the head covering and of the long hair: one symbolizes her submission while the other symbolizes her glory.
The Angels
In verse 10 we are given another reason "For this cause ought the woman to have power (authority) on her head because of the angels.” Why is this? Ephesians 3:10 gives us a clue about angelic observation. God uses the Church to teach them something about His manifold wisdom. God teaches them by object lessons or symbols.
There is simply not enough context in this passage for me to determine what Paul is saying about the angels. (Please understand this is my opinion about that phrase) When a woman prays or prophecys during a church gathering with her head covered, she performs a ministry to the angels. She becomes an object lesson of submission to divine headship. What a rebuke she is to the wicked angels! Their sin is rebellion against divine authority. What a delight to the obedient angels, as they see also the man’s head uncovered portraying the unshielded glory of God and His accepted authority!
Culture
There are some who argue that this was a symbol that was understood by the people of Corinth at the time this was written, and therefore because our culture doesn't understand the meaning it is no longer necessary for a woman to practice this. The problem I have with this approach is that none of the reasons Paul gives are cultural. Also I have a major concern about dismissing any practice that is spoken about in scripture without some other part of scripture giving an explanation of why we should dismiss it. Such as the civil and ceremonial laws of the old testament. This is not an old testament command. This is right in the middle of the new testament teaching about order in the church.
What about verse 16
“But if any man seem to be contentious, we have no such custom, neither the churches of God.” some will point to vs 16 and claim that Paul is saying that we don't have this custom in the church therefore to avoid contention don't worry about what I just said if you don't want to do it. My problem with this interpretation is I don't believe anything unimportant is included in scripture. (2 Timothy 3:16,17) Paul did not just waste ink when writing the first part of this passage. I believe the correct interpretation of this verse is. If anyone in the church is being contentious and trying to refuse this teaching. They should know that the churches of God do not have the custom of women not covering their heads or of men covering their heads.
