"The priest of the Old Law
was a figure of Him;
while the priest of the New Law
works in His person." (St. Thomas Aquinas)
This means that when the priest acts in consecrating bread and wine it is also Christ acting by becoming present in his divinity and humanity under the appearances of bread and wine.
The priest who represents Christ must therefore be a male not a female since a woman representing Christ would be a fiction. The Son of God was conceived with a male nature, died on the cross as man, rose from the dead with his male nature and now sits at the right hand of the Father forever as the God-Man.
Some would allow women priests on the grounds that through Baptism we all share in the priesthood of Christ. While this is true, it is only the priest who is ordained to act in the person of Christ the head. All other Christians can only share as members in offering the Sacrifice of Christ. The priesthood is a separate sacrament and he only can act in Persona Christi. "Other Christian denominations to justify ordaining women, have had to change the understanding of the nature of the priesthood from one which conveys an indelible spiritual character on the man who is ordained to one in which the priesthood is treated as a mere function." (About.com/Why Can't Women Be Priests in the Church?)
Some try to convince us that women should be ordained because they are equal to men. Yes, we are both equal in so far as we have intelligence and free will. At the same time we are not equal in gender because we have different roles in the world. God did not create human nature neutral; you are either man or woman and your way of feeling, thinking and acting reflect this difference. Man or woman is who we are; it is our essence. Transgender is an anomaly, something not intended by God, rather the result of human sin. Jennifer Ferrara, a former Lutheran minister who became a Catholic states, "A mothers and fathers are not interchangeable. Women are not men and, therefore, cannot be priests anymore than they can be fathers in the physical sense. If women can step into the role of priest, then it is no longer one of fatherhood." (wetn.com, "Farmer Lutheran Pastor Debunks Women's Ordination")
Feminists point to Paul's Gal. 3:28 to justify their stand which reads,
is neither Jew nor Greek,
there is neither slave nor free person,
there is not male and female;
for you are all one in Christ Jesus."
In this passage Paul did not have the equality of woman in mind, rather, he is pointing out that "When we humans of any and every description come into Christ sincerely, we are equally and wholly in Him and are thereby saved irrespective of who we are, where we are, or what we are." (Bibleviews.com/The Real Meaning of Galatians 3:28) St. Paul is in this passage not speaking of the role of men and women in the Church.
Others try to make a case for women priest on the grounds that we had diaconesses in the early Church, but does this means? Epiphanus of Salamis (c. 377 AD) made this statement, "It is true that in the Church there is an order of deaconesses, but not for being a priestess, nor for any kind of work of administration, but for the sake of the dignity of the female sex, either at the time of baptism or of examining the sick or suffering, so that the naked body of a female may not be seen by men administering sacred rites, but by the deaconess." (catholic.com/Women and the Priesthood/Catholic Answer)
In the early Church there were Orders of Virgins, Widows and Diaconesses but none of them were ordained to the priesthood.
8. Role of Woman in the Church