I don't know.....using the word "patriarchy" to describe the Holy Trinity seems in error to me. God is gender-less (even though we use the metaphor of Father). All of humanity is made in God's image. When we emphasize the Father only (in the Trinity) we miss the community and sharing of love and distinction that's represented in the Trinity--the paradox of 3 in 1. To me....it really seems to minimize all that's revealed to us in the Trinity. Our entire ability to love others has to do with what we believe about the Trinity. No one should be excluded or perceived as less valuable.
I really appreciate the writing of Mike Morrell and Fr Richard Rohr. Together they wrote the Divine Dance (which is based on the Cappadocian Father's Trinity). It seems the modern church has gotten away from that Trinity. In Mike Morrell's blog, he wrote:
Father, Son and Holy Spirit are all referred to as masculine. The error is in referring to God the Mother.
This is not an error in metaphor. This is an error theology.
Who 'Father' is and who 'Mother' is refers to more than just words and symbols. These are concepts that have been written into our very psyches through millions of years of evolution. Religions that worship God the Mother change everything about God. Ultimately, those religions become about worship of Nature and fertility rites, and even sacred prostitution. The become involved with Magik and the manipulation of nature to the neglect of morality.
Motherhood is not really a moral choice after all. For nine months, mother and child are one biological unit. Childhood is imbued into the nature of the feminine.
To be a father though, involves the moral choice of choosing to stay with the mother and child for those nine months and beyond, and to chose to lead the family.
Thinking about it from an evolutionary point of view, what we might infer from the idea that our physiologies developed specialized sperm cells to be killer cells of other males sperm in utero is that being a provider and a protector of the family unit of mother and child is not nature's choice for us. Being a father, being a Patriarch of the family, goes beyond the way that our physiologies have evolved. Our physiology is that of breeders, but not fathers.
Feminism describes the Patriarchy in the most negative and incendiary of terms, as if it involves the exercise of raw power of the man over the woman. God, who is Trinity, describes the patriarchy in a way that is totally opposite of this. Patriarchy is not about aggrandizement of power, but of submission to love. Patriarchy is not power; it is love. Patriarchy is fatherhood. Fatherhood involves choosing to be a father, to assume the role of father, ando provide for one's family rather than choosing to maximize one's pleasure and move on, as is the nature of the beast.
It is no coincidence that the advent of feminism has corresponded to the rise in hook-up culture, and the demise of fathers in the family unit. Really, where else could a movement that denigrates patriarchy lead to?
It Is God in all three persons who serves as our example of what fatherhood means.
Of course it is not about Spirit being imbued with male genitals. Further, atonement, the at-one-ment of God becoming man so that man may become God, is as inclusive of women as it is of men. Before Adam and Eve became separate they were together, and it was only sin that estranges man from woman.
But none of that means that recognizing God as Father father and not mother is mere metaphor and word play.
There is no error in describing God as Father, and if father then patriarch, which is synonymous with Father.
And who has seen the Son has seen the Father. The mystery of God is that God is One, Father, Son and Holy Spirit too.