Jesus instituted an all-male priesthood because each priest is to act In Persona Christi—in the Person of Christ. Christ is the high priest, and a man is ordained into His priesthood. Jesus is true God and true man, fully divine and fully human. He has a divine nature and a human nature. His human nature has a gender like any other human nature, and his gender was male. As God, He is pure spirit without gender, but in his humanity, Jesus Christ is a man. The Priest who acts in the person of Christ needs to be male in order to represent the God-Man.
At the Last Supper, our Lord ordained twelve of His apostles in the fullness of the priesthood. If it was our Lord’s intention to ordain women, He certainly would have ordained one of the countless women who followed Him when He preached all over Palestine. His mother, Mary, was His most faithful and obedient disciple, yet she was not chosen to be an apostle. Martha and Mary were close to Christ and were loyal followers, but neither of them became apostles, either. For women to be allowed to be instructed, to be preached to, and to be in conversation with our Lord was a radical concept for the first-century Jewish religion. Not only were women faithful followers, but wealthy women often funded the expeditions of our Lord and His apostles, so it wouldn’t have been inconceivable for our Lord to ordain women.
We therefore have to look at the theology behind the all-male priesthood. First, no one, male or female, deserves to be a priest. It is a gift freely bestowed by God. When a man is ordained to the priesthood, his dignity does not lie in himself, but in the fact that he shares in the priesthood of Jesus Christ. It is Christ who is the priest, using the sacramental priesthood as the vehicle to confer grace. For example, the holy sacrifice of the Mass is the same sacrifice of Calvary (but in an unbloody manner); it is Jesus who is priest and victim at every Mass.
Second, we need to look at the theology of creation in which God created man and woman as equals but with distinct roles. Pope John Paul II wrote an encyclical letter on women. In this letter, he mentions that woman have a rightful calling that should not be overshadowed by the concept of women clergy. Instead, it is important to develop their role as generative and maternal. Only a woman can bear and bring forth children. Naturally, women possess qualities of nurturing. In his letter to women, he also notes that women who do equal work should also get equal pay and equal opportunities in employment and education. This is where equality of the sexes must be defended. However, man and woman have distinctive roles; one is not better than the other, rather they complement each other. To deny a woman’s role in salvation is to deny her femininity.
Third is the theology of the Church. The Church is always noted in the feminine: she, Holy Mother Church, the bride of Christ. Saint Paul refers to Jesus as the bridegroom. Christ loves the Church as a groom loves his bride. The spousal relationship even goes back to Old Testament times, when God ordered the prophet Hosea to marry the prostitute Gomer. She was an unfaithful spouse, and Hosea was the faithful husband who kept taking her back no matter how many times she fell. This marital relationship was to symbolize the relationship between God and His chosen people who had time and time again become unfaithful, engaging in idolatry and false worship of pagan gods. Since a priest shares in the one priesthood of Jesus Christ, then the references of the Church as mother and priests as father connect; thus priests take on the masculine role of fathers.