Nobody, including St. Paul, is talking about something one sided. The passage in I Cor 11 actually mentions the mutuality of the sexes.
For if a woman be not covered, let her be shorn. But if it be a shame to a woman to be shorn or made bald, let her cover her head.  The man indeed ought not to cover his head, because he is the image and glory of God; but the woman is the glory of the man.  For the man is not of the woman, but the woman of the man.  For the man was not created for the woman, but the woman for the man.  Therefore ought the woman to have a power over her head, because of the angels.  But yet neither is the man without the woman, nor the woman without the man, in the Lord.  For as the woman is of the man, so also is the man by the woman: but all things of God.
St. Paul writes of the natural order among the sexes in the earlier verses of the passage, but, in verse 11 and 12, also writes of their reciprocity in the Lord. These two aspects of the relationship between the sexes do not contradict each other.