This answer builds upon and expands upon Jayarathina's answer
The following article does not include the reality though that Jayarathina brought up. This reality is that priestesses were common amongst the Pagan world, so for Christ to not have done so, it gives even more reason for why the Catholic Church does not ordain women (it is simply following the example of Christ
Priestly Ordination to Men Alone
The reason that women cannot be priests is theological and obviously historical as well. In his Apostolic Letter Ordinatio Sacerdotalis, Pope Saint John Paul II talks about the reservation of priestly ordination to men alone. He mentions that it is not in the authority of the Church to ordain women priests, he states “I declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgment is to be definitely held by all the Church’s faithful.”1
The Nature of Priestly Ordination to Men Alone
1) A priest acts in “persona Christi” He is another Christ. Christ was a man and by that very nature a women being a priest would be incompatible. (The nature of the priesthood)
2) The scriptural accounts regarding the Gospels, of Christ choosing his apostles only from amongst men (The Scriptural Basis)
3) Throughout the centuries, even up to this day, the Church’s living and teaching authority has held that the exclusion of women from the priesthood is in accordance with God’s plan (The Tradition of the Church)
A priest acts in “persona Christi” he is literally a second Christ. The son of God became flesh as a man, and therefore the priest’s maleness is essential to his priestly role. It is also to be held that although equal in dignity, the very nature of man and woman is different.
The fact is that women and men though equal in dignity in the eyes of God have different functions according to their vary nature. For example, “men were created to be focused more in the exterior, while women in the interior, men tend to look more on the physical, women more in the human person, men are mostly the provider, women the nurturer of the family, men are paternal, women tend to be maternal”2
This helps explain that the reservation of priestly ordination to men, is by no means a sort of anti-women attitude that the Church has against women. No rather it has to do with the very nature and the differences of those two natures between male and female.
Mary DeTurris stated “Pope Saint John Paul II has written and spoken often about the equality of women, their unique gifts and their role in the Church. The pope affirmed women’s central importance in history and said the Church believes the Gospel message of Christ is “ever relevant” when it comes “to setting women free from every kind of exploitation and domination.”3
DeTurris further explained that the role of the Virgin Mary was drastically different from that of the Apostles and Disciples. DeTurris stated “ The fact that the Blessed Virgin Mary, Mother of God, and Mother of the Church, received neither the mission proper to the apostles nor the ministerial priesthood clearly shows that the non-admission of women to priestly ordination cannot mean that women are of lesser dignity, nor can it be construed as a discrimination against them”4
The role of women in Church in Church and in the faith itself, is to be pursued by following in the footsteps of Mary. Mary grew in sanctification through her own personal holiness, by doing the will of God in her life. Her ceaseless prayers, for the Church and her own holiness in her daily life is basically that of the women’s role.
Tradition and Scripture
First and foremost Saint Pope John Paul II states in his Apostolic Letter Ordination Sacerdotalis that in the Gospels themselves, Jesus chooses his disciples only amongst men. He further states that this has been the tradition of the Church even up to the present day. Pope John Paul states:
“The Church holds that it is not admissible to ordain women to the priesthood for very fundamental reasons. These reasons include: the example recorded in the Sacred Scriptures of Christ choosing his Apostles only from among men; the constant practice of the Church, which has imitated Christ in choosing only men; and her living teaching authority which has consistently held that the exclusion of women from the priesthood is in accordance with God’s plan for his Church”5
Similarly the Catechism of the Catholic Church states:
“Only a baptized man (vir) validly receives sacred ordination.” The Lord Jesus chose men (viri) to form the college of the twelve apostles, and the apostles did the same when they chose collaborators to succeed them in their ministry. The college of bishops, with whom the priests are united in the priesthood, makes the college of the twelve an ever-present and ever-active reality until Christ’s return. The Church recognizes herself to be bound by this choice made by the Lord himself. For this reason the ordination of women is not possible. (CCC 1577)
The Early Church and the Church Fathers
Ever since the early church, leading up to the second and third century, there were heretical groups of Christians that started ordaining women to work priestly functions. Various Church Fathers and councils quickly condemned this practice as contrary to the nature of the priesthood.
Saint John Chrysostom
“[W]hen one is required to preside over the Church and to be entrusted with the care of so many souls, the whole female sex must retire before the magnitude of the task, and the majority of men also, and we must bring forward those who to a large extent surpass all others and soar as much above them in excellence of spirit as Saul overtopped the whole Hebrew nation in bodily stature” (The Priesthood 2:2 [A.D. 387]).
“When a widow is to be appointed, she is not to be ordained, but is designated by being named [a widow]. . . . A widow is appointed by words alone, and is then associated with the other widows. Hands are not imposed on her, because she does not offer the oblation and she does not conduct the liturgy. Ordination is for the clergy because of the liturgy; but a widow is appointed for prayer, and prayer is the duty of all” (The Apostolic Tradition 11 [A.D. 215]).
Council of Nicaea I
“Similarly, in regard to the deaconesses, as with all who are enrolled in the register, the same procedure is to be observed. We have made mention of the deaconesses, who have been enrolled in this position, although, not having been in any way ordained, they are certainly to be numbered among the laity” (Canon 19 [A.D. 325]).
Council of Laodicea
“[T]he so-called ‘presbyteresses’ or ‘presidentesses’ are not to be ordained in the Church” (Canon 11 [A.D. 360]).