The above question gets to the heart of Catholic theology regarding the nature of the priesthood.

There have been pressure (from mainly infiltrators), suggestions, debates and enquiries from within and outside the Church, on the ordination of women to the Catholic priesthood. Let us start from the beginning.

In the Old Testament, Israel believed that the title of priesthood was bestowed by God on biblical Aaron and his male offspring forever as an eternal covenant. As the God of Israel is eternal, His trust and covenant are likewise - including the priestly covenant.

God said to Moses;

“Then bring near to you Aaron your brother, and his sons with him, from among the sons of Israel, to serve me as priests. Aaron and Aaron’s sons, Na'dab and Abi'hu, Elea'zar and Ith'amar. And you shall make holy garments for Aaron your brother, for glory and for beauty. And you shall speak to all who have ability, whom I have endowed with an able mind, that they make Aaron’s garments to consecrate him for my priesthood. (Exodus 28:1-3) RSV-SB

Israel believes that the male inheritors of the priesthood are the male descendants of Aaron. These men are known to Israel as Kohanim. The Kohanim are blessed in Jeremiah along with the greater tribe of Levi. (Jeremiah 33:18-23)

Now,  coming to the New Testament, the teaching of the Church is that, priests are supposed to represent the likeness of Jesus Christ, a male figure. The Catholic argument is therefore that women are not suitable to represent the male figure of Christ. Within the Catholic institution, the Popes reinforce what they view as biblical law demanded by God. (1 Tim 2:12-13, 1 Tim 3)

The Theology of In Persona Christi

This is the most significant theological argument. The Church teaches that the priest acts in persona Christi (in the person of Christ) when celebrating the Eucharist. The priest is not just a representative or a stand-in; he is a sacramental icon of Christ.

The Holy Mass which the priest celebrates is the same as the sacrifice of Christ on Calvary. Not another sacrifice. We enter into that same one. That is why in 1 Corinthians 10:16,  St. Paul says,

The cup of blessing which we bless, is it not a participation in the blood of Christ? The bread which we break, is it not a participation in the body of Christ?

 It was not a woman who hung on the Cross on Good Friday, it was Christ, a male.

Another significant point is that, Christ is the Passover Lamb as we are told by St. Paul in 1 Corinthians 5:7:

 For Christ, our Passover lamb, has been     sacrificed.

God gave specific instructions to Moses about the qualities of the Passover lamb in Exodus 12:5

Your lamb shall be without blemish, a male, a year old; you shall take it from the sheep or from the goats.

We can see clearly that the lamb of sacrifice which prefigured Christ had to be male, as commanded by God.

So, to repeat, Jesus did not ordain any women. He selected all of His Apostles, and non were women. It is not true that he acted to the culture of the day. For all we know, Jesus did not hesitate to condemn what was wrong with the customs and culture of His time. Look at the woman caught in adultery. (John 8:7). If that were true, we will be accusing him of  sexism. He interacted freely with women. ( Mt 9:20; Lk 7:37-39; Jn 4:27)

Apostolic Tradition

The Church teaches that the apostles, in turn, followed Christ’ example. Throughout the early Church, there is no record of women being ordained as priests (presbyters) or bishops.

The idea of priestesses was not unknown to Jesus since it was a common practice in religions of His time and culture, though not in Judaism.

 Mary His mother would have been most ideal, if He wanted priestesses. Mary could have spoken the words of consecration literally; 

“This is my body, this is my blood.”

No one, including the Pope, has the authority to change the designs of the Church which Christ instituted. If anyone pretends to do, it will be null and void and of no effect at all.

Specifically, the Church is unable to change the substance of a sacrament.  You for example cannot be baptised in wine, nor may a substance not bread be used for the Consecration at Mass. If invalid martial is used, then the sacrament does not take place. Likewise, since the priest acts in the person of Christ, the Church has no authority to confer the sacrament on those who are unable to represent the male Jesus Christ.

In many cultures in Nigeria and beyond, the roles of the sexes are very distinct and clear, and they may not be interchangeable. In marriage ceremonies for instance, whether a Native Law marriage, or a Sacramental church wedding, where the father of the bride is not present, a male from the father’s family usually presents the bride to her husband. A female can never play that role. There have been occasions where a younger male sibling has had to play the role of father by presenting her elder sister, in the absence of an older male in the father’s family. Not even a mother can play that role. It is not discrimination against women. Women also have some roles which a man cannot play.

Didn’t the early Church ordain women?

There are books available in book stores that claim to have found evidence of the early Catholic Christian Church ordaining women.

Some early Christian women belonged to orders of Virgins, widows and deaconesses which are forerunners of modern nuns. However, none of these was ordained to the priesthood.

In 1994, the then Pope, John Paul II, now St John Paul II, put a final seal on the discussion and query on whether a woman can be ordained to the priesthood or not.

“......Wherefore, in order that all doubt may be removed regarding a matter of great importance, a matter which pertains to the Church’s divine constitution itself, in virtue of my ministry of confirming the brethren, (Luke 22:31-32), I declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgement is to be definitively held by all the Church’s faithful.” ( Ordinatio Sacerdotalis 4) JP. II, 1994

I hope that Pope St. John Paul II's declaration will put an end to the question/agitation for female priesthood, which answer is very clear from Scripture, Sacred Tradition and Reason(Common sense).