I’m currently reading Philip B. Payne’s 2023 book, The Bible vs. Biblical Womanhood: How God’s Word Consistently Affirms Gender Equality, published by Zondervan. I want to share a few lines about what he says in it about head coverings vs. hairstyles in 1 Corinthians 11:2–16.
I see a few things (slightly) differently from Dr Payne regarding this passage, which has traditionally been understood as being about head coverings for women. We both agree, however, that the issue is most likely problematic hairstyles of the men and women who were praying and prophesying in Corinthian churches.
Dr Payne writes that Paul wanted the women to wear their long hair bound up, which was how socially respectable Roman women wore their hair in the first century. Here is how he summarises his arguments supporting the idea that hairstyles, rather than a cloth covering for women, is Paul’s concern in 1 Corinthians 11:2–16.
Several statements in these last few verses should remove any doubt that hair is the covering Paul is talking about. [See 1 Cor. 11:14–15.]
First, Paul would not have written “Judge for yourselves” if he was requiring women to wear a garment, because Hellenistic women are usually not depicted [in ancient art] or described [in ancient literature] as wearing a head-covering garment, so they would certainly not judge this as improper. 
Second, he affirms that “if a woman has long hair, it is her glory.” Nothing in the immediate context indicates that hair is a glory that should be covered. Rather, Paul affirms that long hair is her natural glory. This affirmation would undermine Paul’s argument if he intended that women should cover their hair with a garment.
Third, he affirms that “long hair is given to her as a covering.” Here for the first and only time in this paragraph [i.e. 1 Cor. 11:2–16], Paul uses the word for a head-covering garment. He does it, not to require one, but to assert that a woman’s hair has been given to serve as a head covering. Therefore, when a woman’s hair is put up modestly over her head, her head is covered. A woman does not need to put a garment over her head to “cover” it.
The Bible vs. Biblical Womanhood, pages 72–73.
Dr Payne believes the issue in Corinth was long hair on some men and unbound hair on some women that could be understood as signalling sexual availability: the primary issue being morality. I suggest the problematic hairstyles were longish hair on men and short hair on women that signalled sexual renunciation: the primary issue being reputations in broader society. Maybe it’s a bit of both, morality and reputations.
Whatever the case, in both our views, gender distinctions were being blurred by hairstyles that were socially suspect in first-century Corinth. And we both agree that the women who were praying and prophesying did not need to cover their heads with any kind of garment.
The Bible vs. Biblical Womanhood is much shorter and much easier to read than Dr Payne’s detailed book Man and Woman, One in Christ: An Exegetical and Theological Study of Paul’s Letters, published in 2009. His new book is written for a general audience with the aim of countering flawed interpretations of scripture that continue to be used to restrict capable women.
Dr Payne writes that “This book is for those who care deeply what the Bible teaches. It is especially for those struggling to reconcile the Bible’s seemingly contradictory teachings about men and women.” It’s a worthwhile read, and suitable for people exploring this topic for the first time and for those who have been listening to discussions and debates on “biblical womanhood” for a while.
 I received my copy of gratis from Dr Payne via Zondervan with no obligation to recommend the book.
 “Certainly” seems too strong a word when speaking about the attitudes of a congregation from 2000 years ago.
 Many English translations add a word that means “veil” in 1 Cor. 11:10, but Paul does not use any such a word in the Greek of this verse.
 We know from 1 Corinthians 7 that some Corinthians were giving up on marriage and sex. And there are stories in the Apocryphal Acts of women cutting their hair and dressing as men when they renounced marriage and sex (e.g., Acts of Thecla). (See also my reply to Amy’s comment here.)
1 Corinthians 11:2–16, in a Nutshell
Head Coverings and 1 Corinthians 11:2–16
A Note on Nature and Hairstyles in 1 Cor. 11:14–15
“Uncover-Cover” Words in 1 Corinthians 11:2–16
4 reasons “head” does not mean “leader” in 1 Cor. 11:3
All my articles on 1 Corinthians 11:2–16 are here.
Hair Lengths and Hair Styles in the Bible
A wife has no authority of her own body? (1 Cor. 7:4)