In his Apostolic Letter Ordinatio sacerdotalis (1994), the Holy Father Pope John Paul II, declared that “the Church has no authority whatsoever to confer priestly ordination on women and that this judgment is to be definitively held by all the Church's faithful.” This definitive statement leaves no “wiggle room” for those who would like to continue debating the question. As the Congregation for the Doctrine of the Faith made clear in 1995, the statement that the Church has no authority to ordain women as priests, is not merely a matter of Church discipline (which can be changed), but belongs to the deposit of faith (which cannot). “This teaching requires definitive assent, since, founded on the written Word of God, and from the beginning constantly preserved and applied in the Tradition of the Church, it has been set forth infallibly by the ordinary and universal Magisterium (cf. Second Vatican Council, Dogmatic Constitution on the Church Lumen Gentium 25, 2). Thus, in the present circumstances, the Roman Pontiff, exercising his proper office of confirming the brethren (cf. Lk 22:32), has handed on this same teaching by a formal declaration, explicitly stating what is to be held always, everywhere, and by all, as belonging to the deposit of the faith” (Congregation for the Doctrine of the Faith, Concerning the Teaching Contained in Ordinatio Sacerdotalis).
This Apostolic Letter alludes to the reasons given in the Declaration Inter Insignores, by the Congregation for the Doctrine of the Faith in 1976. They include, in addition to the testimony of Scripture and Tradition, the example of Christ, who though counter-cultural in many respects, continued Israel’s tradition of a male priesthood in reserving the Office of Apostle to men. That the Apostles did not regard this as a divine oversight is evident from the fact that they themselves ordained only men. And so the Church has continued this Sacred Tradition down to the present.
The question why women can't be ordained priests is often confused with the issue of equality. The Holy Father has made it clear that men and women (as far as their sex is concerned) are equal before God (e.g., Mulieris Dignitatem 6). But equality isn't identity. Men and women have different though complementary functions. Priesthood is a male function, for the reason that a priest is an icon of Christ, and Christ is male. The maleness of Christ is an important sign of His relationship to the Church, His Bride. As in nearly all cultures a man takes the initiative in winning a wife, so Christ took the initiative in winning souls and establishing His Church. For this reason, marriage is a “mystery” or sacrament of the Church (Eph 5:32).
St. Paul develops this theme in his parallel between a local church and the family. A "bishop" (or "overseer," which applied to both bishops and priests in NT times) is expected to keep his own family in order, "for if a man does not know how to manage his own household, how can he care for God's church?" (1 Tim 3:5) Male headship in the family is an axiom of both Scripture and Tradition, and if the Church is the Household of God, and Christ is Head of the Church, then His headship in the Church can be represented only by men.
However, lest it seem that God has honored men above women, we should recall that of all created beings, including the hierarchy of Angels, God raised a Woman to the highest place, the Blessed Virgin Mary. Though she was not an Apostle, she was made Queen of the Apostles, Queen of Angels, Queen of the universe, and the Mother of her own Creator.