Millennia ago, the most revered of all wise men who had studied all of their lives the written law realized that they had a problem. They had been given rather unclear set of rules - which left plenty of room for interpretation. The debated among themselves, "How many steps can one take before it is considered a journey?" "Is it permissible for a man to search for a lost sheep on a day of rest?" "What tasks can be done that are not considered work?" Their collected wisdom was passed down from teacher to student, that is from rabbi to disciple as spoken wisdom; known as the oral law.
Part of the oral law was Jewish practice - the customs that made the Israelites distinct from their neighbors. In it were all sorts of rules that were important because they were deduced from the written law even though they were the sorts of things that were not clearly stated in it.
The earliest Christians were also Jewish, they would have been familiar with the Written Law (particularly Genesis, Exodus, Leviticus, Numbers, and Deuteronomy), the oral law (the Mishna and the Gemara, which make up the Talmud - it would eventually be written down; but at this point it was not), and they would have been interested in the teachings of Jesus and the apostles (likewise, they would eventually be written down, but at this point they had not.)
There was a group of early Christians who believed that new converts ought to be made 'fully Jewish' in order for them to be 'truly Christian'. They were known as the Judaizers, and they spent much of their time suggesting that circumcision and teachings from the Talmud ought to be main-stays of Christianity. In Acts 15, the Council of Jerusalem is called to resolve the matter. The verdict? No circumcision.
For the most part, people don't really pay attention to what the Judaizers do after that. But I think I can display pretty good evidence that they didn't stop causing trouble. Remember the Corinthian church?
What I mean is this: One of you says, “I follow Paul”; another, “I follow Apollos”; another, “I follow Cephas”; still another, “I follow Christ.” (verse 12)
Paul - a roman citizen, a jew, a Pharisee-turned Apostle, from Tarsus
Apollos - a jew, from Alexandria
Cephas - the Latin variation of Peter, Jesus' Apostle
Christ - referring to Jesus, this is a Greek word
Corinth was located on a Greek peninsula, but it was controlled by the Romans (whose language was Latin). It also seemed to have more than one school of thought reguarding Jewish teachings. Each group of people had their favorite, likely the one that most closely matched their group - Jews following either Paul or Apollos, Romans following Cephas, and Greecians following Christ. It's difficult to say whether it was Paul's teachings or Apollos' teachings that attracted the favor of the Judaizers - but throughout 1 and 2 Corinthians Paul goes to great lengths to make his stance on their teachings clear. Same goes for Galatians; just because they lost on circumcision, they pushed their ideas about following Jewish practice particularly about the role of women in the early church.
Women should remain silent in the churches. They are not allowed to speak, but must be in submission, as the law says. If they want to inquire about something, they should ask their own husbands at home; for it is disgraceful for a woman to speak in the church. (1 Cor. 14)
http://womenofthewall.org.il/kol-isha/ - kol isha has been translated to mean the voice a woman is nakedness and therefore is forbidden. This is taken seriously as to prevent female singers from singing in the prescence of those to whom they are not related.
Culturally speaking, when a person is having a discussion in public, questions are expected to be asked of them. The problem isn't so much that women listen to the discussion, but the possibility that she might ask a really good question. We can see that the Old Testament never requires women to be silent. In fact, they are even permitted to undertake a nazarite vow (so long as their husbands or fathers agree to it.) We can see that in the Bible Lydia spoke and even hosted guests at her house. Apollos learned a thing or two from Priscilla and Aquila. Wouldn't it be terribly ironic of it were Apollos' followers that were keen on silencing women even knowing that a woman had taught Apollos himself? Then again, Paul himself did correct Peter when it came to his decision to eat with 'the circumcision group' in Galatians 2; so it's quite possible it was Cephas who had the following of the Judaizers all along.
For if a woman does not cover her head, she might as well have her hair cut off; but if it is a disgrace for a woman to have her hair cut off or her head shaved, then she should cover her head. (1 Cor. 11)
The following women are divorced, and do not receive [the amount of] their Ketubah:—She who violates the Law of Moses, or Jewish [rules]. What constitutes [a violation of] the Law of Moses? If she causes him to eat [food] which has not paid tithe: if she submits to his embraces while she is in a state of Niddah: if she does not set apart Chalah: and if she vows, but does not keep [her vow]. What constitutes [a violation of] Jewish rules [customs]? If she goes out with her hair loose [bareheaded]: if she spins in the street, and converses [flirts] with any man. Abbah Saul saith, "[Likewise] if she curses his children in his presence." R. Tarphon saith, "[Also] if she is a קולנית, a noisy woman." What is [meant by] a noisy woman? One who speaks in her own house [so loud] that the neighbours can hear her.
Given Paul's reference to the oral law, we must assume that the influence of the Judaizers had created a situation in which the women were darned if they did and darned if they didn't; the practice of head covering as well as the law requiring silence were Jewish practices, but the Corinthian church wasn't entirely Jewish. Roman men had a custom of covering their heads as they tended to their priestly duties, Roman women had the tendency to wear elaborate hairstyles with braides and bits of gold woven into their hair, Greek men and women didn't really wear anything on their heads, and Jewish men wore prayer shawls while women were required to have their heads covered in public at all times. These three distinct cultures did have Christianity in common, but precious little traditions common to them to bind them together. Remember how Paul told the believers that while it was not a sin to eat meat, they shouldn't in the prescence of a weaker brother? I thinke he used the same logic to deal with the Judaizers. It was not a sin to not wear head coverings, but because these sisters in the faith really had no choice, their Greek and Roman sisters ought to also wear them and that none of the men ought to wear them so that they are consistent in practice. It seems more like a compromise to me: "have it your way if the you want the women to wear them, but if you want to make it a matter of honor and shame, then you can't do what they do; you'll have to go without. Not only that, but so long as women follow the standards of decency, they can pray and prophesy." Paul was brillant that way.
But I suspect that he'd tell us the same things he did to the Galatians: "You foolish Americans! Who has bewitched you? Why are you so proud that you force women into silence and are trying to reintroduce headcoverings? Is the law that which saves you or the grace of the power of your beliefs what set you free?"