Don

1Co 11:7

For a man should not have his head covered, since he is the image and glory of God. But the woman is the glory of the man.

I had an insight, so want to put it here.  I think Paul is discussing a conflict a woman has in this verse that a man does not have.  Here Paul confirms that a man should not cover his head, this argument should also apply to a woman, except there is 1 more factor.  All women are made in the image of God and all believing women reveal the glory of God (2 Cor).  So she should not cover her head, just like a man.

However, a woman is ALSO the glory of the man, or a wife is the glory of her husband.  A wife is supposed to cover her head to indicate she is married, at least she is supposed to cover in public, with strange men around.  So she has a conflict, she should be cover and not cover in church, which was a semi-public gathering.

So my take is this is why Paul give her the choice, she can decide what is best, knowing the specific circumstances at any specific time.