Blessed John Paul II's Apostolic Letter, Ordinatio Sacerdotalis, spells out the Church's reasons for promoting an all-male priesthood:
When the question of the ordination of women arose in the Anglican Communion, Pope Paul VI, out of fidelity to his office of safeguarding the Apostolic Tradition, and also with a view to removing a new obstacle placed in the way of Christian unity, reminded Anglicans of the position of the Catholic Church: "She holds that it is not admissible to ordain women to the priesthood, for very fundamental reasons. These reasons include: the example recorded in the Sacred Scriptures of Christ choosing his Apostles only from among men; the constant practice of the Church, which has imitated Christ in choosing only men; and her living teaching authority which has consistently held that the exclusion of women from the priesthood is in accordance with God's plan for his Church."(1)[...]Read the whole letter here; it is quite brief and clear about the principles at hand.
The presence and the role of women in the life and mission of the Church, although not linked to the ministerial priesthood, remain absolutely necessary and irreplaceable. As the Declaration Inter Insigniores points out, "the Church desires that Christian women should become fully aware of the greatness of their mission: today their role is of capital importance both for the renewal and humanization of society and for the rediscovery by believers of the true face of the Church."(10) [...]
Although the teaching that priestly ordination is to be reserved to men alone has been preserved by the constant and universal Tradition of the Church and firmly taught by the Magisterium in its more recent documents, at the present time in some places it is nonetheless considered still open to debate, or the Church's judgment that women are not to be admitted to ordination is considered to have a merely disciplinary force.
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 (cf. Lk 22:32) I declare that the Church has no authority whatsoever to confer priestly ordination on women and that this judgment is to be definitively held by all the Church's faithful.
It is also clear from this news article that Fr. Bourgois dissents from this long-standing Church teaching in a way that puts him wholly outside of the Catholic Church, and which makes it imperative for the Church to begin the process of removing him from the priesthood:
But Bourgeois said he cannot publicly recant, as his order requires. "What they're asking me to do is lie," he said in an interview from his home in Columbus, Ga. "To say I don't believe God calls women to the priesthood as well as men -- I cannot do that." [...]I can't help but think that Fr. Bourgeois sees himself as a courageous person standing up against some sort of unjust institutional power; this would not be surprising, as some elements in the Maryknoll order have for years been infected by radical Marxism, liberation theology, and similar leftist notions, such that it becomes tempting for some in that order to cast all struggles in these sorts of terms and ideas. It's much more boring to call Bourgeois a budding heretic--and yet, if we are quite honest about where his pro-female ordination ideas will take him, that is exactly what he ought to be called. If he believes that the Church does not speak for Christ with the voice of the Holy Spirit; if he believes that ordination is some sort of "right" which women are unjustly being denied; if he believes that the Church is an oppressor who must be defied--then he is no longer really Catholic in his thoughts and actions, is he?
Bourgeois released his reply, saying “I believe that our Church’s teaching that excludes women from the priesthood defies both faith and reason and cannot stand up to scrutiny.
“This teaching has nothing to do with God, but with men, and is rooted in sexism. Sexism, like racism, is a sin. And no matter how hard we may try to justify discrimination against women, in the end, it is not the way of God, but of men who want to hold on to their power.”
And if he were a really honest person, Fr. Bourgeois would not only refuse to recant, but would eagerly help the Church process his laicization and formal separation from the Church, so he could in good conscience join some other church that has no problem with female ministers. But dissenters aren't really honest: because what they really want is to retain their positions and jobs and careers within the Church while denouncing her teachings, setting themselves in opposition against her, and making splashy, public, media-darling nuisances of themselves. In this they are no different from CINO politicians who remember that they were baptized Catholic before each important election--but never when it might inconvenience their moral actions--or like "once Catholic" celebrities who use their baptismal certificates as their credentials by which to bash the Church at every opportunity.
Larry D at Acts of the Apostasy has been keeping an eye on this story and especially on obtaining the names of those priests who have signed statements in support of Fr. Bourgeois. Larry promises to let us know each of these priests' current parishes and dioceses as soon as he has that information available; I think this is the right sort of action to take, so that each priest's bishop can be contacted. Given that some of these priests have fairly common names, too, it's important that scandal not be given in places where some priest who fully supports all Church teaching has the misfortune to share a name with a dissenter.
The bottom line for me is this: if I ever thought that the Church herself was so seriously in error about a grave matter dealing with faith or morals (and the question of the male priesthood, impacting as it does the bridal imagery in Holy Scripture, is certainly a serious matter of faith), I would have a clear course of action before me. First, I would pray, and seek the private counsel of those more learned in the matter; next, I would do as much reading and research as possible; and finally, if it were not possible for me to accept the Church's teaching even with the assent of faith, I would mention my struggles in sacramental Confession and ask whether I must absent myself from Communion (not from Mass, of course) until my conscience could somehow resolve the issue. Only if I became convinced that the Church is not who she says she is, the Bride of Christ, the Church instituted by Christ as the ordinary means of salvation for all, would I consider leaving--but even as I write that, I have to admit that I can't ever see that happening; I've had ample opportunity to consider the Church's claims, and have always found them both reasonable and worthy of faith.
What I would not do is make a public spectacle of my dissent in a way intended to embarrass the Church (but actually only embarrassing me, in the long run). Dissenters who do that sort of thing have already, to me, reached the point where they no longer wish to be united to the Church--even if that desire is hidden, or in conflict with the desire to retain the offices and powers which the Church has already granted them.