Genesis 3:
16 To the woman He said,
“I will greatly multiply
Your pain in childbirth,
In pain you will bring forth children;
Yet your desire will be for your husband,
And he will rule over you.”
God said the above!
We also have to consider the implication of husband and wife being one flesh, as per Jesus' comment.
A certain part of the one flesh has a different function to the other parts, but they all need to work together for the good of the whole.
There are parts of the body that can be regarded as weak spots, and vulnerable to attack by an enemy. Paul was just reminding the men and women in the church of this fact. He was in effect asking men to exercise their responsibilities as head of the family and spiritual leaders of the church of God. In order for the men to be able to exercise these responsibilies, Paul was more or less asking the women not to offer opinions on scriptural matters and matters of leadership in the church unless it's with members of their own gender, but discuss them by all means in private with their husbands. This doesn't infer that women are inferior to men, but each gender has God given roles and responsibilities that must be met, and never deferred or usurped.
Now, I'm talking about members of the church of God here. For any other church, yes, go ahead and make your own arrangements if you will, but be warned that Jesus will not be in your midst.