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. 4 Every man who prays or prophesies with his head covered dishonors his head, 5 but every wife who prays or prophesies with her head uncovered dishonors her head, since it is the same as if her head were shaven. 6 For if a wife will not cover her head, then she should cut her hair short. But since it is disgraceful for a wife to cut off her hair or shave her head, let her cover her head. 7 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. 8 For man was not made from woman, but woman from man. 9 Neither was man created for woman, but woman for man. 10 That is why a wife ought to have a symbol of authority on her head, because of the angels. 11 Nevertheless, in the Lord woman is not independent of man nor man of woman; 12 for as woman was made from man, so man is now born of woman. And all things are from God. 13 Judge for yourselves: is it proper for a wife to pray to God with her head uncovered? 14 Does not nature itself teach you that if a man wears long hair it is a disgrace for him, 15 but if a woman has long hair, it is her glory? For her hair is given to her for a covering.
-1 Corinthians 11:3-15

"Does the Bible teach that women have to wear a cloth head covering when praying?"

No. This passage is about headship: the authority/submission structure of married couples and how it relates to prayer and prophecy. It’s not referring to literal heads or pieces of cloth. They’re symbols/metaphors intended to illustrate authority and submissiveness (1 Corinthians 11:10). Even Paul’s mention of hair length on literal heads in verse 5 is presented as an analogy ("it is the same as") to make the point that it’s dishonorable for a wife to have her head uncovered (to not be under her husband’s authority). In the metaphor, head represents authority and covering is to "cover" your own authority with someone else's, meaning you submit to them.

The reason this passage is so confusing and debated is because it introduces a lot of ideas and metaphors at once. It talks about headship, head coverings, hair length, dishonor, glory, order of creation, authority, praying/prophesying, and angels. Peter acknowledged that some of Paul’s writings were hard to understand (2 Peter 3:16) and this passage is no exception. However, it can be understood through careful study. Below is a verse by verse breakdown, explaining what I believe Paul was trying to communicate. 

Verse by verse explanation of 1 Corinthians 11:3-15

Verse 3: This verse establishes the authority structure of headship. The head of a wife is her husband, the head of every man/husband is Christ, and the head of Christ is God the Father. Other passages also say Christ is the head of the church (Colossians 1:18), which is lead by men. Christ’s relationship with the church is communicated to mankind through earthly marriage as a metaphor (Ephesians 5:32. Revelation 19:7). As a side note, headship has nothing to do with value or importance. We know this because God the Father has headship over Jesus, yet Jesus is equal to Him (John 5:18,10:30)

Verse 4: If a man prays or teaches with his head covered, he dishonors his head (Jesus.) A man‘s head (headship) is covered when his wife has authority over him or he neglects his responsibility of authority. The reason this dishonors Jesus is because it goes against God’s object lesson of headship.

Verse 5: If a wife prays or prophesies (declares God’s word) with her head uncovered (meaning she doesn’t submit to her husband as her head/authority), she dishonors her head (husband). By doing so, she doesn’t give her husband the chance to live out his God-given leadership role.

Verse 6: Paul compares this lack of submission with another metaphor: the shame that came from a woman shaving her head in those days. He’s saying if a wife refuses to be under her husband’s authority, she might as well shave her head since it will have the same disgraceful effect. To avoid this disgrace, she should submit to her husband, which is to metaphorically cover her head (submit to him).

Verse 7: The reason the husband shouldn’t cover his head (be under his wife’s authority) is because he’s "the image and glory of God", while the wife is "the glory of man". Marriage is a metaphor of Christ’s relationship to the church; the husband represents Christ and the wife represents the church (all believers) (Ephesians 5:32). When a faithful marriage accurately represents Christ’s relationship with the church, the husband who represents Christ brings Jesus/God glory, and the wife who represents the church (believers) brings mankind (specifically the church) glory. In doing this, they both glorify God. Since both men and women are made equal in God’s image (Genesis 1:27, Galatians 3:28), we know this isn’t saying that man is more valuable than woman or that woman is made in man’s image. That’s why the passage leaves out "image" when speaking of women being the glory of man. 

Verses 8-9: Paul points to the order of creation to explain why husbands represent Christ and have authority, and why wives represent the church and submit to him (cover her head). Man was created first so he represents Christ. Had women been created first and man come from her, it would be the other way around. However, that isn’t how God chose to create us. Furthermore, God represents himself as male in scripture and Jesus became a man. That’s why man was chosen to have authority and represent Christ in the marriage/headship metaphor.

Verse 10: Another reason given for this "symbol of authority " (the metaphor of head coverings to communicate authority/submission) is that we’re being observed by the angels, who also learn theological truths about Christ and his relationship to the church through this symbol of authority. One of the main purposes for marriage is to teach theological truth to observers, both human and angelic. When a husband has authority over his wife yet loves her in a self-sacrificial way, it gives us a picture of how Christ loved us and sacrificed himself for us. 

Verses 11-12: Paul included a disclaimer to ensure that people don’t get the wrong idea and think men are superior to women just because they were created first and have been given the role of authority. He pointed out that although men were created first, they are now born of women. The phrase "all things are from God" reminds man that he’s not the creator of woman or greater than her in any way. Men and women are equals created in God’s image. 

Verses 13-15: Paul again points to hair length as an illustration of his point. He highlights what he sees as the obvious conclusion: that it’s improper for a wife to pray without being under her husband’s spiritual authority. In fact, she brings herself glory by covering her head (being under husband’s authority) similar to the way women often get glory from long, beautiful hair. 

1 Corinthians 11:3

"What does it mean that a husband is the head of his wife?"

Headship in marriage means that the husband is his wife’s spiritual leader and protector. His role is to help her grow in sanctification while loving and serving her sacrificially, as Christ loved and served the church (believers) (Ephesians 5:25-30). Headship is a metaphor/object lesson God uses to communicate spiritual truths. In marriage, it demonstrates that Jesus loves the church and the church submits to him. For more on headship, click here. 

1 Corinthians 11:3

"If a husband is the head of his wife, does this mean he's greater than her?"

No. The title "head "cannot mean greater than because the same title is used of God the Father being head over Jesus, yet Jesus is one with the father and completely equal to Him (John 5:18, John 10:30-38) Furthermore, other passages make it clear that men and women are equals created in God’s image (Genesis 1:27, Galatians 3:28). Headship in marriage is simply an object lesson meant to to communicate spiritual truths.

1 Corinthians 11:7

"If man is the image and glory of God and woman is the glory of man, is this saying that men are greater than women?"

No. Whatever this passage means, we know it can’t be teaching that men are greater than women since the Bible is clear that they’re both made in the image of God (Genesis 1:27, Galatians 3:28). That’s why  the word "image' is omitted when it says woman is the glory of man. 

1 Corinthians 11:9

"This passage says that women were made for men, but men weren't made for women. Isn't that basically calling them property?" 

No. Paul is simply stating that the order of creation supports his point about head coverings (headship and authority). Man was created first, and woman was created from man (Genesis 2:18-24). Paul used this to support his point that God intended husbands to be head of their wives and represent Christ in the metaphor, not the other way around. This doesn’t make men better than women or make her his property. The following verses (1 Corinthians 11:11-12) were intended to make sure readers didn’t think men were somehow superior to women. They point out that although woman originally came from man, now every man is born of a woman.

1 Corinthians 11:13-15

"Does this passage teach that women must have long hair and men must have short hair? Why would it otherwise be disgraceful?"

No. Paul used hair length as an analogy to make his point that shame comes from undermining God’s order of headship (authority/submission). Verse 5 makes it clear that this is an analogy ("it’s as if her head were shaven"). Just as a woman gets glory from having long beautiful hair, she gets glory from being under the authority of her husband the way God intended. Likewise, when a man tries passing off his authority responsibilities to his wife, it brings disgrace to him the way trying to wear a woman’s hairstyle would. This analogy isn’t a commentary on how men and women should wear their hair, it’s simply taking the familiar concept of gender based hairstyles and furthering the head analogy. Although women have generally had longer hair than men in most societies throughout history, there certainly are exceptions. For example, Samson and those who took the vow of the  Nazarites weren’t disgraced by having longer hair. The disgrace comes from trying to mimic the opposite gender, not the hair length itself. I think his would have been very clear the original audience.