
Bro. Tom Forde, OFM Cap, an Irish Capuchin, has an illuminating article entitled Why Women Can't Be Priests on his highly recommendable blog Breathing With Both Lungs.
Promoting vocations to traditional Catholic societies, institutes, and religious orders using the Extraordinary Form of the Roman Rite for men and for women.

6. Let the seminaries be jealously guarded in order that a proper atmosphere will be maintained. Let them always be destined exclusively for preparing youths, not for civil careers, but for the noble vocation of being ministers of Christ. Let philosophy, theology, and the related sciences, especially Sacred Scripture, be studied along the lines of pontifical directives: according to the teaching of Saint Thomas which Our venerable Predecessor so often recommended, and We Ourselves recommended in the Apostolic Letter of January 23, 1904.[Cf. ASS, 36:467 ff.] Therefore, let the Bishops exercise the most prudent vigilance towards the professors' teachings. Let them recall those who run after certain dangerous novelties to their sense of duty. If they do not profit from these warnings, let them be removed-cost what it may -- from their teaching position. Young clerics are forbidden to frequent the universities unless the Bishops think there are very good reasons and necessary precautions have been taken. Seminarians are absolutely forbidden to take part in external activities. Accordingly. We forbid them to read newspapers and periodicals, excepting, in the case of the latter, those with solid principles and which the Bishop deems suitable for their study. Let discipline continue to be fostered with renewed vigor and vigilance. Finally, in every seminary there must be a spiritual director. He is to be a man of extraordinary prudence and experienced in the ways of Christian perfection. With untiring zeal he must train the young men in solid piety, the primary foundation of the spiritual life. Venerable Brethren, if these rules are conscientiously and religiously followed they will be your sure guarantee of seeing a clergy growing up around you which will be your joy and your crown.
7. If these instructions are not observed, the problem of insubordination and independence which We now lament will be even more aggravated by some of the younger clergy and cause even more harm. This is especially so since those who are subject to this reprobate spirit are not lacking, and, abusing the sacred office of preaching, they are its outspoken promoters and apostles, to the detriment and scandal of the faithful.
On 11th June, 1905, Pope St. Pius X issued his Encyclical Letter Il Fermo Proposito to the Bishops of Italy on Catholic Action in Italy:
25. The priest, raised above all men in order to accomplish the mission he has from God, must also remain above all human interests, all conflicts, all classes of society. His proper field of action is the Church. There, as ambassador of God, he preaches the truth, teaching along with respect for the rights of God respect also for the rights of every creature. In such a work he neither exposes himself to any opposition nor appears as a man of factions, ally to one group and adversary to others. In such a way he will not place himself in the danger of dissimulating the truth, of keeping silence in the conflict of certain tendencies, or of irritating exasperated souls by repeated arguments. In all these cases he would fail in his real duty. It is unnecessary to add that while treating so often of material affairs he may find himself obligated to perform tasks harmful to himself and to the dignity of his office. He may take part in these associations, therefore, only after mature deliberation, with the consent of his Bishop, and then only in those cases when his assistance will be free from every danger and will be obviously useful.
26. This does-not diminish his zeal. The true apostle must make himself "all things to all men"[I Cor. ix:22] in order to save all. Like the Divine Redeemer, he ought to be moved with compassion, "seeing the crowds . . . bewildered and dejected, like sheep without a shepherd."[Matt. ix:36] By means of the printed and spoken word, by direct participation in the above-mentioned cases, he can labor on behalf of the people according to the principles of justice and charity by favoring and promoting those institutions which propose to protect the masses from the invasion of Socialism, saving them at the same time from both economic ruin and moral and religious chaos. In this way the assistance of the clergy in the works of Catholic Action has a truly religious purpose. It will then not be a hindrance, but rather a help, to the spiritual ministry by enlarging its sphere and multiplying its results.
On 15th April, 1905, Pope St. Pius X issued his Encyclical Letter Acerbo Nimis on the teaching Christian Doctrine:
8. We do not think it necessary to set forth here the praises of such instruction or to point out how meritorious it is in God's sight. If, assuredly, the alms with which we relieve the needs of the poor are highly praised by the Lord, how much more precious in His eyes, then, will be the zeal and labor expended in teaching and admonishing, by which we provide not for the passing needs of the body but for the eternal profit of the soul! Nothing, surely, is more desirable, nothing more acceptable to Jesus Christ, the Savior of souls, Who testifies of Himself through Isaias: "To bring good news to the poor he has sent me."[11]
9. Here then it is well to emphasize and insist that for a priest there is no duty more grave or obligation more binding than this. Who, indeed, will deny that knowledge should be joined to holiness of life in the priest? "For the lips of the priest shall keep knowledge."[12] The Church demands this knowledge of those who are to be ordained to the priesthood. Why? Because the Christian people expect from them knowledge of the divine law, and it was for that end that they were sent by God. "And they shall seek the law at his mouth; because he is the angel of the Lord of hosts."[13] Thus the bishop speaking to the candidates for the priesthood in the ordination ceremony says: "Let your teaching be a spiritual remedy for God's people; may they be worthy fellow-workers of our order; and thus meditating day and night on His law, they may believe what they read, and teach what they shall believe."[14]
10. If what We have just said is applicable to all priests, does it not apply with much greater force to those who possess the title and the authority of parish priests, and who, by virtue of their rank and in a sense by virtue of a contract, hold the office of pastors of souls? These are, to a certain extent, the pastors and teachers appointed by Christ in order that the faithful might not be as "children, tossed to and fro and carried about by every wind of doctrine devised in the wickedness of men," but that practicing "the truth in love," they may, "grow up in all things in him who is the head, Christ."[15]
11. For this reason the Council of Trent, treating of the duties of pastors of souls, decreed that their first and most important work is the instruction of the faithful.[16] It therefore prescribes that they shall teach the truths of religion on Sundays and on the more solemn feast days; moreover during the holy seasons of Advent and Lent they are to give such instruction every day or at least three times a week. This, however, was not considered enough. The Council provided for the instruction of youth by adding that the pastors, either personally or through others, must explain the truths of religion at least on Sundays and feast days to the children of the parish, and inculcate obedience to God and to their parents. When the Sacraments are to be administered, it enjoins upon pastors the duty to explain their efficacy in plain and simple language.
12. These prescriptions of the Council of Trent have been summarized and still more clearly defined by Our Predecessor, Benedict XIV, in his Constitution "Esti minime." "Two chief obligations," he wrote, "have been imposed by the Council of Trent on those who have the care of souls: first, that of preaching the things of God to the people on the feast days; and second, that of teaching the rudiments of faith and of the divine law to the youth and others who need such instruction." Here the wise Pontiff rightly distinguishes between these two duties: one is what is commonly known as the explanation of the Gospel and the other is the teaching of Christian doctrine. Perhaps there are some who, wishing to lessen their labors, would believe that the homily on the Gospel can take the place of catechetical instruction. But for one who reflects a moment, such is obviously impossible. The sermon on the holy Gospel is addressed to those who should have already received knowledge of the elements of faith. It is, so to speak, bread broken for adults. Catechetical instruction, on the other hand, is that milk which the Apostle Peter wished the faithful to desire in all simplicity like newborn babes.