The Catholic Church can be seen by many, including members from within her walls, as being antiquated and discriminatory in its view that the ordained priesthood should be reserved to men. I wonder how many people have left their home in the Catholic Church for another denomination based in large part on this topic.Sunday night St. Mary Seminary and Graduate School of Theology in the Diocese of Cleveland held their annual Mullen Lecture in which Missionary of the Blessed Sacrament Sister Sara Butler, a member of the Vatican’s International Theological Commission, discussed “The Ordination of Women and the Witness of Tradition.” Formally a strong believer in the ordination of women, Sr. Butler has come not only to accept but also to believe in the Church’s teaching that the ordained priesthood should be reserved to men and that the Church has no authority to do otherwise. There is not enough room here to report everything that she said, but allow me to give the basic argument.
In the Old Testament there is no evidence of women offering sacrifices as a mandate from God. There is a similar lack in the New Testament. Even Mary was not chosen for the priesthood for whom it would have been most fitting. Of course, priesthood is not a reward, and so we take this a step further in noting that Jesus had among his personal companions and disciples many women and he did not pick from them either. In His freedom to choose as He desired He reserved this parituclar office to men and it was not from lack of candidates who were female, worthy, and capable. So the question becomes if the quality of being male in representing Christ is essential to state of the priesthood (as opposed to looking at the mere function of the priesthood.) Is it an indispensable factor such a water being necessary for baptism or bread and wine being needed for the Eucharist? It is the constant and universal Tradition of the Church that this is so. No women were chosen to replace the apostles as bishops or priests and neither has it occurred in the history of the Church that such a thing has happened and been sanctioned. When it did happen it was immediately and universally condemned as was with the case of the two women who were “ordained to the Catholic priesthood” this past Sunday. We actually do not recognize anything as actually having taken place. The two retain the same status they had as before the ordination. 
Now, the talk did not touch on the “why” of the question, just the “that”. And it is the case that the Church has consistently believed and taught that it has no authority to do differently in this regard and the strongest argument comes from that Tradition. Scripture alone cannot completely support a male only priesthood (which might show why there is such a difference in the Protestant theology.) Sacred Tradition, which testifies to the unyielding witness to this belief, plays a fundamental role and cannot be ignored in Catholic theology. All arguments to the contrary, and there are some very good arguments, will ultimately come to rest up against this obstacle and it would be dangerous to ignore the importance of Tradition for Catholics as it is one of the fundamental pillars of the Church. Destroying the pillar in this instance risks destroying it in all instances.
In the end we see the male priesthood as being instituted by Christ and that we have maintained His will from Apostolic times on, which has been testified to by the constant and universal
Tradition of the Church, by Scripture, and upheld consistently by the magisterium.If you would like to read more on the topic, you might want to pick up Sr. Butler’s book, “The Catholic Priesthood and the Ordination of Women.”
