Read an interesting link from Monergism on headcovering by Dr. Robert Spinney. He makes an interesting point on our presuppositions regarding headcovering for women. There are basically two presuppositions we come to 1 Corinthians 11 with. One is that we presuppose (presupposition A) that Paul was writing only to the Corinthian church and the default position should be that headcovering is not normative for today unless proven otherwise.. The other presupposition (presupposition B) is that we should assume that headcovering is normative for today unless proven to not be. From Dr. Spinney's post...
Presupposition B is more sound. This is the assumption we normally use when we interpret the Bible. For example, pastors do not begin sermons on “children obey your parents in the Lord” by proving that such instruction is applicable to Christians today. We all assume (correctly) that such teaching passages are applicable unless we have strong biblical reasons for believing otherwise.
Regarding 1 Corinthians 11:1-16, this means that we must see solid evidence that we are not supposed to do this today before we reject the instruction. The burden of proof rests upon the man who says we do not have to obey this biblical command.
Unfortunately, we don’t treat the issue of head coverings in this manner. We place the burden of proof upon those people who maintain that we should obey the Bible’s instructions in 1 Corinthians 11:1-16. We would never do this with other instructions in the Word of God. Why the double standard? Perhaps because obeying this particular instruction might mark one as peculiar. Our strong desire to fit in with our prevailing culture may well influence how we interpret the Bible. Surely this is a danger that we must guard against. (emphasis added)
The entire article is thought provoking and worthwhile reading. Advocating headcovering is not a knee jerk reaction, a simplistic and overly literal reading of the Bible. Many Christians have studied the issue and come to the conclusion that women should cover their heads. It is at the very least an issue that should be prayerful considered and not dismissed because this person or that person has passed judgment over the issue and that means the matter is closed. If you assume that any command in the Bible must be defended first, you throw every doctrine in the Bible in doubt and insist that the burden of defense falls on the Word to fit into our culture first unless we can prove otherwise.
In fairness, there are several articles linked from Monergism's subsection on headcovering that do not support headcovering. I would invite you to read those articles and consider what they have to say but that you test all things against what the Word says.