I agree with your post Balaam's ass, and Jimmy Carter gives an insightful comment recognising that earlier forms of Christianity (and there were many) did not prevent women from officiating. It is worth understanding that Christian cults were mainly the domain of the poor and powerless which included women who by gender alone, were considered to be of low status. Therefore for women to be given a voice within the church was a big plus; a rise in status.
It was the principle in Imperial Rome which asserted its power over so much of Late Classical Europe and the Near East which demanded male dominance as an expression of Imperial function. As the Roman world came severely under threat from outsiders, it was politically expedient to fuse the various Christ cults and form a new State religion-- and assert the Roman male dominance principle and determine the selection of "Christian" texts in line with Imperial thinking. Earlier the image of the "manly God of war" in the Hebrew scriptures was simply echoing the long held patriarchal principle.
Divergent cultures over time and in different locations have produced social systems, some with matrilineal property inheritance and other important rights for women but there are no cases known to anthropology with exclusively female control.
We might construe this was due to the child bearing and nurturing role of women contrasted with the apparent need for males to excel at arms and defend their people.
Let's face it, this gender division and male authority drawn from it, no longer holds true in the advanced societies today. The inflexible governing body are very unlikely to modernise unless there is money in it for them.