Why do women in the church of Christ overseas don't cover their heads during worship? Is there any difference between Nigerian women and your own people? Nigerian women who worship with your people discovered that they do not all cover their heads during worship.
I'm not in a position to speak for all the brethren in the United States, but there are women who cover their heads during worship and there are those who do not. At one time, head covering was taken for granted, even among denominations, though the forms of that covering varied with fashions. Being a thing that everyone did because everyone else did it, people lost knowledge of why it was done. After all, when everyone agrees, it doesn't generate much discussion. But fashions changed; hats and other forms of head coverings became old-fashioned in the United States. Most fashion historians put it down to the 1950's when hair care products made keeping one's hair looking good inexpensive.
The demise of head coverings brought the issue of the necessity of women covering their heads back to the forefront, but there was not a solid conclusion among the brethren. Some of arguments against the head coverings that I have heard are:
Long hair is an acceptable alternative to an artificial covering. This particular argument is not used as often these days as most agree that the text talks of a covering in addition to the long hair women wear. Paul uses the length of women's hair to argue that an added veil should not be seen as an unreasonable request.
It only applies to prophetesses (women who prophesy). Since prophecy has ended, the need for the veil has ended as well. The difficulty is that Paul speaks of wearing the veil when woman prophesies or prays. While prophecy has ended, praying has not. In addition, the purpose of the veil is stated to be a sign of submission. Women being under the authority of men has not ended.
It was a local custom in Corinth and Paul is arguing that the Corinthian women should not violate their local customs. The difficulty here is that there doesn't seem to be proof that it was a local custom at the time Paul wrote to the Corinthians. Images in the Roman catacombs indicate that women covering their heads during prayer was widely practiced in the years after Paul wrote to the Corinthians. The basis of the argument is caused by the vagueness of the wording in I Corinthians 11:16. The sentence can be translated two different ways, depending on how a person reads the context. You could read I Corinthians 11:16 to say that the church has no other custom, but for women to wear a head covering during prayer and prophecy. Or, you could read it to say that the church has no such custom of applying a local practice to all the churches. I have difficulty with the later reading because it basically cancels all the arguments that Paul just made and they were based on historical and global principles, not local practices.
The wearing of the veil is a sign of submission, but that submission must be voluntarily given. It behooves preachers to encourage men and women to follow the roles God has given each of them. Forcing women to wear a veil will not make them any more or less submissive to their duties. Hence, while I encourage the practice, I understand there are those who have doubts about the need or are convinced that it is not necessary. Since a woman not wearing the veil does not hinder my worship or the worship of my family, I am content to take a long term approach to the issue. Where I worship, there are women who chose to wear veils and those who chose not to. They understand why each made their choice. It is something that is discussed at various times, but neither feel that the others' choice impacts their personal relationship with God.