Here is what St Thomas has to say regarding the ordination of women (listen to the podcast above to get my commentary on his thoughts).
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.
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.