As heavycola pointed out, it's hard to base an argument on just one person alone. Paul is a nice guy, an Apsoitle, but he is only one person. The Catholic Church, like that man who stood on the roof with the fiddle, relies on tradition. When everyone says "NO" you don't suddenly say, "YES."
The following comes from
Catholic Answers. You can see that in the early church the question was indeed asked and the answer was a resounding "NO."
Hippolytus
"When a widow is to be appointed, she is not to be ordained, but is designated by being named [a widow]. . . . A widow is appointed by words alone, and is then associated with the other widows. Hands are not imposed on her, because she does not offer the oblation and she does not conduct the liturgy. Ordination is for the clergy because of the liturgy; but a widow is appointed for prayer, and prayer is the duty of all" (The Apostolic Tradition 11 [A.D. 215]).
The Didascalia
"For it is not to teach that you women . . . are appointed. . . . For he, God the Lord, Jesus Christ our Teacher, sent us, the twelve [apostles], out to teach the [chosen] people and the pagans. But there were female disciples among us: Mary of Magdala, Mary the daughter of Jacob, and the other Mary; he did not, however, send them out with us to teach the people. For, if it had been necessary that women should teach, then our Teacher would have directed them to instruct along with us" (Didascalia 3:6:1–2 [A.D. 225]).
Firmilian
"[T]here suddenly arose among us a certain woman, who in a state of ecstasy announced herself as a prophetess and acted as if filled with the Holy Ghost. . . . Through the deceptions and illusions of the demon, this woman had previously set about deluding believers in a variety of ways. Among the means by which she had deluded many was daring to pretend that, through proper invocation, she consecrated bread and performed the Eucharist. She offered up the sacrifice to the Lord in a liturgical act that corresponds to the usual rites, and she baptized many, all the while misusing the customary and legitimate wording of the [baptismal] question. She carried all these things out in such a manner that nothing seemed to deviate from the norms of the Church" (collected in Cyprian’s Letters 74:10 [A.D. 253]).
Council of Nicaea I
"Similarly, in regard to the deaconesses, as with all who are enrolled in the register, the same procedure is to be observed. We have made mention of the deaconesses, who have been enrolled in this position, although, not having been in any way ordained, they are certainly to be numbered among the laity" (Canon 19 [A.D. 325]).
Council of Laodicea
"[T]he so-called ‘presbyteresses’ or ‘presidentesses’ are not to be ordained in the Church" (Canon 11 [A.D. 360]).
Epiphanius of Salamis
"Certain women there in Arabia [the Collyridians] ... In an unlawful and blasphemous ceremony ... ordain women, through whom they offer up the sacrifice in the name of Mary. This means that the entire proceeding is godless and sacrilegious, a perversion of the message of the Holy Spirit; in fact, the whole thing is diabolical and a teaching of the impure spirit" (Against Heresies 78:13 [A.D. 377]).
"It is true that in the Church there is an order of deaconesses, but not for being a priestess, nor for any kind of work of administration, but for the sake of the dignity of the female sex, either at the time of baptism or of examining the sick or suffering, so that the naked body of a female may not be seen by men administering sacred rites, but by the deaconess" (ibid.).
"From this bishop [James the Just] and the just-named apostles, the succession of bishops and presbyters [priests] in the house of God have been established. Never was a woman called to these. . . . According to the evidence of Scripture, there were, to be sure, the four daughters of the evangelist Philip, who engaged in prophecy, but they were not priestesses" (ibid.).
"If women were to be charged by God with entering the priesthood or with assuming ecclesiastical office, then in the New Covenant it would have devolved upon no one more than Mary to fulfill a priestly function. She was invested with so great an honor as to be allowed to provide a dwelling in her womb for the heavenly God and King of all things, the Son of God. . . . But he did not find this [the conferring of priesthood on her] good" (ibid., 79:3).
John Chrysostom
"[W]hen one is required to preside over the Church and to be entrusted with the care of so many souls, the whole female sex must retire before the magnitude of the task, and the majority of men also, and we must bring forward those who to a large extent surpass all others and soar as much above them in excellence of spirit as Saul overtopped the whole Hebrew nation in bodily stature" (The Priesthood 2:2 [A.D. 387]).
No seriously there used to be a general prohibition among the Orthodox preventing women from receiving communion when they were having their period because they were uncomfortable with the thought of a flow of blood after receiving the Blood of Christ. Western stigmatiasts who were priests (Padre Pio is a good modern example) would have probably driven them crazy.
