I would question the idea of “rule over’ rather than “rule with’. It’s a matter of positions not persons. Just as the Father is not greater as a person than the Son the same applies to male and female.They work as one.
A woman being silent during a gathering together does not just affect the woman during those kinds of ceremonial gatherings used as shadows of the good thing to come. The men there are part of those laws. If the woman does not perform them, the whole congregation shares in the error, vice versa.
I think much has been lost because of the head covering ordinance which is used to represent the new order of government, because the time of the first century reformation had come. This is when the temporal outward form of temple worship as that seen , using shadows and types to preach the gospel in advance, was done away with. The veil which represented the coming of Christ was used express the hidden unseen glory of God who remains without form .
Changing a part of the ordinance or taking away the whole is shown with Arron’s two sons who added something to the law .They both vanished to show the importance of ceremonial laws used to point ahead as the gospel .
The head covering ceremony as shadow points ahead. It is used in a similar way of the veil to show the only glory that should be seen during a gathering together is the glory we see by faith. Take away one aspect of the ceremonial law the rest might as well be dismissed.
This is seen with the breaking of bread ordinance, the head covering /uncovering ordinance was part of the breaking of the bread . It worked to help us understand the marriage supper in heaven when we receive our new incorruptible bodies (neither male nor female Jew or Gentile) . And also a sign for the angels
While we are here on earth again the only glory that should be seen is the hidden glory of God, the purpose of the ceremonial laws.(we walk by faith the unseen) They help us see men and woman share the same outward glory as a manifestation of His. The head covering and the breaking of bread are considered one in principle representing what we will be when we do receive our new incorruptible bodies. Exchanging the bread for Jellow, or chocolate milk to represent the blood of Christ , many today would be offended.
1Co 11:7 For a man indeed ought not to cover his head, forasmuch as he is the image and glory of God: but the woman is the glory of the man.
Man is both an image as a representation and a glory as a manifestation, of His hidden glory. If man does not follow that ordinance to uncover the whole of Corinthians 11 new order is made to not effect. Just as if the woman does not cover her hair.
In the head covering and uncovering doctrine, the woman is not spoken as the image of man but the glory of man.
1Co 11:7 For a man indeed ought not to cover his head, forasmuch as he is the image and glory of God: but the woman is the glory of the man.
Here it is not representation but manifestation. The glory of man must not be manifest in spiritual exercises, we walk by faith. No glory but that of God is to be seen in the spiritual realm. Therefore when the man see the women’s head covered, he is reminded that his glory is covered also . Their public ministry is done so God alone receives the glory .
It’s not who is capable, but will men honor the glory doctrine. As the glory hidden from our eyes. We are not to cover the glory of city on the hill.
And I saw no temple therein: for the Lord God Almighty and the Lamb are the temple of it.And the city had no need of the sun, neither of the moon, to shine in it: for the glory of God did lighten it, and the Lamb is the light thereof. Rev 21:22