Objection 1. It would seem that the female sex is no impediment to receiving Orders. For the office of prophet is greater than the office of priest, since a prophet stands midway between God and priests, just as the priest does between God and people. Now the office of prophet was sometimes granted to women, as may be gathered from 2 Kings 22:14. Therefore the office of priest also may be competent to them.
Objection 2. Further, just as Order pertains to a kind of pre-eminence, so does a position of authority as well as martyrdom and the religious state. Now authority is entrusted to women in the New Testament, as in the case of abbesses, and in the Old Testament, as in the case of Debbora, who judged Israel (Judges 2). Moreover martyrdom and the religious life are also befitting to them. Therefore the Orders of the Church are also competent to them.
Objection 3. Further, the power of orders is founded in the soul. But sex is not in the soul. Therefore difference in sex makes no difference to the reception of Orders.
On the contrary, It is said (1 Timothy 2:12): "I suffer not a woman to teach (in the Church),* nor to use authority over the man." [The words in parenthesis are from 1 Corinthians 14:34, "Let women keep silence in the churches."]
Further, the crown is required previous to receiving Orders, albeit not for the validity of the sacrament. But the crown or tonsure is not befitting to women according to 1 Corinthians 11. Neither therefore is the receiving of Orders.
I answer that, Certain things are required in the recipient of a sacrament as being requisite for the validity of the sacrament, and if such things be lacking, one can receive neither the sacrament nor the reality of the sacrament. Other things, however, are required, not for the validity of the sacrament, but for its lawfulness, as being congruous to the sacrament; and without these one receives the sacrament, but not the reality of the sacrament. Accordingly we must say that the male sex is required for receiving Orders not only in the second, but also in the first way. Wherefore even though a woman were made the object of all that is done in conferring Orders, she would not receive Orders, for since a sacrament is a sign, not only the thing, but the signification of the thing, is required in all sacramental actions; thus it was stated above (Question 32, Article 2) that in Extreme Unction it is necessary to have a sick man, in order to signify the need of healing. Accordingly, since it is not possible in the female sex to signify eminence of degree, for a woman is in the state of subjection, it follows that she cannot receive the sacrament of Order. Some, however, have asserted that the male sex is necessary for the lawfulness and not for the validity of the sacrament, because even in the Decretals (cap. Mulieres dist. 32; cap. Diaconissam, 27, qu. i) mention is made of deaconesses and priestesses. But deaconess there denotes a woman who shares in some act of a deacon, namely who reads the homilies in the Church; and priestess [presbytera] means a widow, for the word "presbyter" means elder.
Reply to Objection 1. Prophecy is not a sacrament but a gift of God. Wherefore there it is not the signification, but only the thing which is necessary. And since in matters pertaining to the soul woman does not differ from man as to the thing (for sometimes a woman is found to be better than many men as regards the soul), it follows that she can receive the gift of prophecy and the like, but not the sacrament of Orders.
And thereby appears the Reply to the Second and Third Objections. However, as to abbesses, it is said that they have not ordinary authority, but delegated as it were, on account of the danger of men and women living together. But Debbora exercised authority in temporal, not in priestly matters, even as now woman may have temporal power.
Source: Summa Theologica (New Advent)