The moment I read that I knew that was wrong, it's the Mormonism in me I guess.
I hunted around and found several different commentaries discussing this passage which agreed with your assessment. Then I found this article from BYU which makes sense to me. It’s written by Sherrie Mills Johnson and called Paul's Teachings in 1 Corinthians on Women.
rsc.byu.edu/archived/shedding-light-new-testament/6-pauls-teachings-1-corinthians-women
As I was reading 1 Cor 11 it this line bothered me,
“…every man praying or prophesying, having his head covered, dishonoureth his head”
Because priest of the Old Testament wore a head covering.
Ex 29:6 6 And thou shalt put the mitre upon his head, and put the holy crown upon the mitre. (see also Zach 3)
So I was questing the reasoning of the passage.
From Johnson article; "Paul next explains that "every man praying or prophesying, having his head covered, dishonoureth his head" ….The Greek text literally says that a man should not pray with anything "hanging down from the head." In other words, it allows for a head covering as long as it doesn’t hang from his head as a veil does…..Traditionally headgear has often served as a symbol of a person’s power….”
I looked it up at Strongs and sure enough that is what it means, a veil hanging down from his head.
The article points out that a head covering is a mark of what one’s authority is; a crown for a king, the Pope’s papal tiara, even a chef’s hat designates an order of rank within the kitchen.
This article explanation is quite to the opposite of what you said;
“It is a symbol of the power that sits over (on) her head. It is a symbol that the man has authority over her.”
From the article;
“Older (and some modern) New Testament commentators claimed that this veiling of women was a sign of her subjection to man. But this does not take into account the context of Paul’s discussion. Both Paul’s words and the style he uses to express those words stress that while there needs to be order there is also equality and interdependence between man and woman as shown in a double chiastic structure:
A For the man is not of the woman;
A' but the woman of the man.
B Neither was the man created for the woman;
B' but the woman for the man.
C For this cause ought the woman to have power on her head because of the angels.
b' Nevertheless neither is the man without the woman,
b neither the woman without the man, in the Lord.
a For as the woman is of the man,
a' even so is the man also by the woman; but all things of God.
The climactic stress placed on the line “
for this cause ought the woman to have power on her head” again tells us that Paul is not speaking of the subordination of women.
While this line has been debated a great deal, and there is no consensus as to what Paul meant, it is obvious that it is not about subjection. Paul goes to such lengths to express the equality and balance of the roles of men and women that for him to be urging the women to be veiled as a symbol of their subjection to men does not fit the context. There is no equality or balance in subjection. In addition, Paul has just stated that according to the line of authority man comes under Christ. If veiling were a sign or symbol that one is under some authority, the man would also be covered
.”
This line is important; 5 But every woman that prayeth or prophesieth….
It’s saying women/wife are capable of taking a role in the family and church, offering prayers and being guided by the Spirit to prophecy. That is significant.
Paul goes on to make a comparison which the Corinthians would have understood;
“..if the woman be not covered, let her also be shorn: but if it be a shame for a woman to be shorn or shaven, let her be covered….But if a woman have long hair, it is a glory to her: for her hair is given her for a covering.”
There is a passage in Num 5:18 which address a woman accused of adultery; “And the priest shall set the woman before the Lord, and uncover the woman’s head,…”
I found this article;
http://www.jewishvirtuallibrary.org/jsource/Judaism/adultery.html
“…..This disarrangement of the hair (usually covered and concealed) may be the origin of the later punishment of shaving a woman's head – more particularly in cases where lesser misconduct, and not the act of adultery, could be proved against her.”
There is another time a woman might have her head shaved and that was when a priest shave her head to check for leprosy. (see Lev 13), This would be a disgrace and cause shame upon her.
Paul is equating the covering or veil with a woman’s long hair which was a symbol of her purity and authority or power to be heard and recognized as an equal to her husband.