The language of verse 11 contrasts with the preceding verses. In several translations, it is worded as, "However, in the Lord...". That "however" negates the previous assertions. Yes, the first woman came from man, but in the Lord, men and women are interdependent.I don't think it contrasts at all. If anything, the passages you're referring to:
Corinthians 11:11 Nevertheless neither is the man without the woman, neither the woman without the man, in the Lord.
12 For as the woman is of the man, even so is the man also by the woman; but all things of God.
Explain that men and women, mankind, are both temporal, fallen beings because both sinned. It is only the "image" and the propriety of exemplifying that "image doctrine" that prohibits women from being in authority in church.
You can't very well assert that the genders are interdependent while simultaneously asserting that all men have "headship" over all women. Further, the "headship" argument applies only s to marriage, and no further.