Why won’t the Catholic Church ordain women as priests?

Regarding whether this could be construed has a kind of discrimination against women, Pope Bl. John Paul II pointed out: “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 discrimination against them. Rather, it is to be seen as the faithful observance of a plan to be ascribed to the wisdom of the Lord of the universe.” (OS, 3)

The Church teaches that men and women “are equal as persons and complementary as masculine and feminine” (CCC, 372). The CDF reminds us that “equality is in no way identity, for the Church is a differentiated body, in which each individual has his or her role. The roles are distinct, and must not be confused; they do not favor the superiority of some vis-à-vis the others, nor do they provide an excuse for jealousy; the only better gift, which can and must be desired, is love (1 Cor. 12-13). The greatest in the Kingdom of Heaven are not the ministers but the saints.” (II, 6)

Both sexes have an indispensible role in the Church: “The New Testament and the whole history of the Church give ample evidence of the presence in the Church of women, true disciples, witnesses to Christ in the family and in society, as well as in total consecration to the service of God and of the Gospel”(OS, 3). Examples include “the holy martyrs, virgins and mothers of families, who bravely bore witness to their faith and passed on the Church's faith and tradition by bringing up their children in the spirit of the Gospel” (MD, 27). Indeed, “the Church is constantly enriched by the witness of the many women who fulfill their vocation to holiness” (MD, 27).

Objection:
Jesus, in choosing only men for the priesthood, was simply following Jewish tradition.  If he were ordaining today, things would be different.

Answer: 

1. Our Lord was anything but a slave to tradition.  He broke with two customs when he asked a Samaritan — and a woman, at that — for water (John 4).  He also urged celibacy on his apostles and dispensed with Jewish ritual when it came to such things as the washing of hands at mealtime (Mt. 19: 12, 29; Lk. 11:38).

2. Had Jesus wished to ordain women, he could easily have done so since there were priestesses at the time in Greece, Egypt, and Rome. 

3. We read in the Letter to the Hebrews that "Jesus Christ is the same yesterday, and today, and forever" (Heb. 13:8).

4. Women have actually exercised as much influence as men in the Catholic Church:

(a) Mary, who is our model, shunned the spotlight. Nevertheless, she remains the most influential mortal in all of Christian history (save for her son, who was God).  

(b) In the United States, no priest or bishop has wielded as much power as Mother Angelica of EWTN fame. 

(c) Mother Teresa of Calcutta overshadowed all Church officials of her day save the pope, and John Paul II was surely one of the most charismatic men in the history of the papacy. Who could compete with him?

(d) As early as the 12th century, a woman by the name of Catherine of Siena outshone everyone else, male or female, when it came to influence over princes and potentates.

(e) Until recently in the West, nuns had a virtual monopoly on the intellectual and moral formation of boys and girls ranging in age from 5 to 14. By the same token, they ran virtually all of the Catholic high schools and colleges for women. Is there any influence comparable to that of the teacher who shapes minds and hearts? And is any group more impressionable than youth?