At this particular point in history, the Roman Catholic Church, the Greek Orthodox Church and certain Protestant churches such as the Southern Baptists and Missouri-Synod Lutherans do not ordain women as priests or ministers.
The feminist movement is vociferous and unremitting in its condemnation as what they perceive as an unfair and outdated dogma, having its origins in an older and ancient patriarchal society. At first glance, the feminists or rather women who are critical of this exclusionary rule could be right. After all, why bar a committed Christian who wishes to serve in and execute this particular office? Why deprive the church of the talent and contribution of half the human race? This argument or rather criticism of this particular rule or dogma I submit fails on a number of grounds.
There are a number of reasons for this particular dogma and those reasons require an understanding of the nature of the priestly or ministerial office and its historical origins and background.
First, the priest or minister who celebrates Mass, the Eucharist or what it is called in the Protestant Church “communion” stands in some sense, in the stead and person of Christ. It is not that a woman cannot be a priest or minister but that she cannot stand in the person of the Divine Savior who revealed himself in his earthly life as a male, and as risen, sits at the right hand of the God the Father in some sort of contiguous, spiritual male body. Thus, it is safe to say that the nature of the re-enactment of the sacrifice of Christ in some sense, whereby the priest or minister stands in the person of Christ, is a male role. It is not that the woman is disqualified politically, constitutionally, or as a matter of justice or fairness from holding this office but that the church, in this particular rule, is not a democracy nor does it operate under the secular rules of apparent fair play. Second, the argument that this doctrine has its origins in outdated patriarchy also fails. In fact, a large part of the ancient world and near East including Assyria, Sumeria, and Babylonia worshipped mother goddesses with out-sized genitals and breasts.
Temple prostitution was common and the reason for this worship of mother goddesses had its origins in our ancestors not knowing how food was grown. Their simple solution was to connect the seasons and growth of food with sexual biological function. Hence, a very common presence in most parts of the ancient world are mother and female earth goddesses.
Jewish culture and its outgrowth in Christianity reject any connection with God and biology and sex.
If God has chosen to reveal himself in female form, he would connect and lead us to believe that as created beings, we are the product of female, maternal and biological function.
In Judaism and Christianity, God chose to reveal himself in male terminology. It was nothing more than an analogy since God is spirit and has no sex or body. If Jesus was the Son of God and God chose to reveal himself in female forms and terminology, then God would be a mother and bearing children rather than Jesus being co-equal and connected equally with God and fully God. In short, for God to be analogized with female sexuality, both we and Jesus would be products of a mother and pregnancy from whom we came and to whom supposedly we go back to. The priestly office is not a job but a sacredotal function and vocation in which the sacrifice of Christ is re-enacted and God chooses not to mislead us to believe that we have some sort of biological relationship to his being.
We are not born of God but rather created by an eternal spirit who, by an analogy, chooses to form his relationship with us through the terms of father and son rather than maternity, pregnancy and birth.
I would add that a minister in the Protestant church, unlike a priest in the Catholic and Greek Orthodox Church, strictly speaking is a leader of a community of Christians and equal among equals rather than one who conducts a sacrifice on a weekly or daily basis as is the case in the Roman Catholic and Greek Orthodox Churches.