From a netfriend:

The problem with this argument is that it depends on the dubious translation of the word avkataka,luptoj Although many lexicons will offer the translation “unveiled”, it is by no means certain that this is the correct translation. It may mean “long hair, flowing down”. The interpretation is further complicated by the possibility that Paul is quoting the Corinthians here and going on to reject their argument. This is strengthened by verse 16 where St Paul states:

But if anyone is disposed to be contentious– we have no such custom, nor do the churches of God.

There was an interesting journal article some time ago by Alan Padgett (sorry, can’t remember the title and the journal – age is catching up with me). Padgett went into the possibilities in great detail and I was convinced by his argument.

Taking into account Padgett’s thesis – of Paul quoting and then rebuffing the Corinthian argument – the translation would run like this:

I praise you because you remember me in all things and hold fast the traditions just as I passed them on to you. And [so] I want you to know that Christ is the source of every man, and God is the source of Christ.

[However, on the basis of this theology you Corinthians argue as follows – I quote you]:

“Every man who prays or prophesies with long hair dishonours his head, and every woman who prays of prophesies with unbound hair dishonours her head, for she is the same as a woman with a shaved head. For if a woman does not keep her hair bound up, let it be cut short. But if it is a disgrace for a woman to have short hair, or a shaved head, let her keep it bound up. For, [as you argue], on the one hand, a man ought not to bind up his hair, being the image and the glory of God.”

However,on the other hand, woman is the glory of man. For man is not from woman, but woman from man. For in fact, man was not created for woman’s sake, but woman for man’s sake [to perfect him]. For this reason, woman ought to have authority over her head, on account of the messengers.

In any case, in the Lord woman is not different from man, nor is man different from woman! And indeed, just as woman is from man, so man is born of woman; and all things are from God.

Judge for yourselves. It is proper for a woman to pray to God with unbound hair. [For] nature does not teach you that long hair is a disgrace to a man. But if a woman has long loose hair it is her glory. For long loose hair is given to her rather than bound up hair.

But if anyone is inclined to be contentious [on this issue], we have no such practice [as you propose], nor do the churches of God.