Here are some reasons to oppose the notion of female cardinals. For the sake of argument, we’re defining “female cardinal” as a woman who is given the canonical right to vote in a papal conclave. Not every cardinal has been ordained, so female ordination (a metaphysical impossibility) is not a necessary condition for a woman being appointed cardinal. It seems to be possible, at least, to appoint a woman as a papal elector. However, here are reasons why the notion is absurd:
1.) Cardinals represent the clergy of Rome, and women can’t be clergymen.
Cardinals are, in their origin and to this day in theory, the clergy of the ecclesiastical province of Rome. The six cardinal-bishops represent the seven Suburbicarian Sees of the Roman province (the Dean of the College of Cardinals holds two such sees, hence the mismatched numbers). The cardinal-priests and cardinal-deacons hold titles around Rome. So, the election of the Pope by the College of Cardinals amounts to the election of the Metropolitan Archbishop of Rome by his suffragan bishops and by his own diocesan clergy. It would be inconsistent to have a woman, who can’t hold any of the titles involved (cardinal-bishop, cardinal-priest, cardinal-deacon). She would be the first cardinal ever to be incapable of becoming a bishop, priest, or deacon.
2.) Cardinals are supposed to be eligible for election to the Papacy.
She would be the first cardinal ever disqualified from election to the Papacy. The idea of a the papal conclave is that someone in that room will be elected Pope. It throws off the entire idea of a conclave to have voting cardinals who are by definition incapable of election themselves.
3.) Someone would *still* try to elect a female cardinal as Pope.
Given the perversity of the human heart, despite any and all directives to the contrary, a number of cardinals would cast invalid votes for a female cardinal. They just would, and when news broke out that the votes were suppressed (and the word would leak out, believe me), there would be public scandal.
4.) Cardinals belong to the hierarchy. Women do not.
Cardinals hold precedence over bishops and archbishops, even if the cardinal himself is only a priest. Why? Because cardinals are the clergy of Rome, and Rome is the supreme See. A (cardinal-)deacon of Rome outranks a non-cardinal Archbishop of Paris, for example. Before Vatican II (I’m not sure about nowadays), cardinals even outranked the Eastern patriarchs.
But what happens when a cardinal not only is not ordained at all, but completely incapable of ordination? A woman lacking Holy Orders officially outranks bishops and archbishops in the hierarchy? This would be a slap in the face to non-cardinals in the hierarchy.
5.) It would encourage the heretical idea of female ordination.
No one outside the Church, and hardly anyone inside the Church, knows what exactly a Cardinal is. They imagine it’s part of some weird gradation of holy orders that goes priest-bishop-archbishop-cardinal-Pope. So, despite the fact that there have been lay-Cardinals before, introducing new female lay-cardinals would give the false impression that women can and should also be ordained priests. After all, if they can hold the greater office, why not the lesser also?
So, it’s a stupid idea. Basta!
P.S. I’m not in principle opposed to cardinals listening to a woman or consulting one in determining whom to vote for, or how to run the Church. St. Catherine of Siena would have been a good person to invite in to speak before a conclave, or to write a letter to the cardinals. She could have dropped some clear hints about what qualities to seek in a candidate. That might require some changes to the procedure, which currently forbids outsiders from dropping in on the conclave or trying to sway the election. So it has its drawbacks, too.