There is an implication in the Bible that women can be more easily deceived than males by Satan.
Because of this, and also because He created a male first, God has given the responsibility of leadership in marriage, and in the church, to men.
I understand that this comment originated from the OP's suggestion that the leadership in marriage is shared, although that might have better been left for an entirely separate thread even if there is more argument for your position than there is mine. My position comes from original Hebrew word understandings of those for father, 'abba,' and mother, 'em.' Both begin with the letter 'alef,' the symbol of leadership. But again, this particular discussion could well generate enough interest for its very own thread.