That God actually created the patriarchal society of the Jews is a shock to many Christians, especially Catholics. That the Hebrews were one small group of Chosen People among many larger and stronger groupings, such as the Hittites and Assyrians, is forgotten, or never understood. The small Hebrew community was organized first under Moses, and then more so under Joshua and the High Priests. Leviticus is a good read for those who want the details. The Covenant came with many rules, but the primary purposes of God, if we can understand the Old Testament in light of the New, was to create a Nation of people who had a system of governance and hereditary priesthood which was male. Matriarchies dotted the ancient world, and one only needs to think of the religious aspects of female priestesses and the rules of sexual engagement these religions demanded. That God intervened and separated this type of occult power and created a People who had male leaders, male priests and the heads of the family were now male. Of course, the feminists hate all this and do their best to undermine this to the detriment of the Church and Church organization.
All of these is a denial of the Incarnation. And, a denial of the Revelation of the Old and New Testament is the keystone of Modernist Heresies. Some Catholics look at the stronger wording of patriarchal theology of the Evangelical Churches and want to remove themselves from those influences and even vocabularies. However, the basis for the patriarchy in the Church cannot be ignored or swept under the carpet. That Christ came as a Man into the world strengthens and indeed, fulfills the patriarchal structures, especially that of priest, as seen clearly in the theology of Hebrews.
That Christ is the High Priest and that an ordained priest is an "alter Christus" has been debated by the feminists for the past thirty years. The Popes who wrote against the Modernist errors warned us of this type of re-reading and reinterpretation of Scripture. That Christ was Divinely Chosen to be a priest, is worth following in the Epistle. I have remarked on the Order of Melchizedeck before on this blog.
The point here is not merely reminding all of the fact of the Incarnation, but that Christ ordained, with the Father and the Holy Ghost, (not the Creator and the Sustainer), that His Church be based on a patriarchal system. One can go back to the Covenant of Abraham and trace the chosing of leadership, through the hereditary and even non-hereditary positions of the sons of the Patriarchs. I say non-hereditary, as some of those chose were not the oldest son, as in the case of David, the King. Solomon was not the oldest son, either.
Some feminists do not want to use the matriarchy, but matristic. Having a woman-centered society involves keeping the maternal side as the controlling unit in passing down land or even names. In a government by mothers, or even women who are unmarried with children, this type of society decides on the rules in families, etc. I have had many Irish friends state that the Celtic families are ruled by the women in the families. I think some of the families in England are matriarchies.