Here is an explanation from Fr Mcnamara about why women cannot become cardinals;
I think we need to distinguish different questions. First, may a woman be appointed cardinal? Second, could women be involved in a papal election? Finally, what is the distinction between archdiocese and diocese?

In response to the first question I would say that the answer is no.

It is true that the cardinalate is a dignity and not a sacred order. It is also true, however, that from the very beginning of the office the cardinals have been associated with the clerical state.

The cardinals are divided into three orders -- bishops, priests and deacons -- even though almost all of them are actually bishops. This is because from a relatively early period the election of the bishop of Rome was restricted to the bishops of the dioceses surrounding the Diocese of Rome: Albano, Sabina-Poggio Mirteto, Porto Santa Ruffina, Velletri-Segni, Frascati, Palestrina and Ostia, which is no longer a functioning diocese and is usually held by the dean of the College of Cardinals.

To these were added the most important priests of the Rome Diocese and the deacons who at that time were relatively few in number and often had the responsibility for its administration. This distribution is still reflected in the distribution of cardinals, of which there are six cardinal bishops, 160 cardinal priests and 39 cardinal deacons.

As time went on the title was widely granted to bishops of other dioceses and those who worked within the Roman Curia. However, the connection with the clergy of Rome was always maintained by granting each cardinal a titular church of which he is, so to speak, honorary parish priest or deacon.

It is true that the title was granted occasionally to those who were not ordained, but not, strictly speaking, to non-clerics. At that time a man canonically entered the clerical state (and the obligation of celibacy) by receiving first tonsure, and this was a minimum requirement for being named cardinal. Unfortunately, some of these behaved more like princes than as clerics and had little intention of proceeding toward ordination.

Others, however, were notable. Pius VII's secretary of state Cardinal Ercole Consalvi (1757-1824) never progressed further than deacon and was already a cardinal a year when the Pope ordained him to this office. It is said that on his way to exile Napoleon Bonaparte remarked that Cardinal Consalvi, who was not a priest, was more of a priest than many who were.

From the time of Pope St. John XXIII, all cardinals should be bishops, but the Pope may and often does grant an exemption to this requirement if requested by the person being named cardinal. In general this has only been granted to those priests nominated after they had passed their 80th year.

Therefore, since the cardinalate is historically tied to the clerical state I would say that this is an impediment to women being named cardinal.

This does not mean that women had no role whatsoever. Women were probably involved in some ways in the election of the bishop in ancient times when this election was done by the assembled faithful. This system produced the occasional St. Ambrose. But it could also provoke deep divisions and was more subject to manipulation by political powers. The system was eventually abandoned.

In some periods in which the power of the state had a strong hand in naming bishops, some queens, such as Isabella of Castile (1451-1504), had no small role in choosing the episcopate even though the appointment fell ultimately upon the pope.

The election of the pope by the College of Cardinals is not of divine right; it has had relatively exclusive rights to papal elections since 1059. However, it is ultimately rooted in very ancient traditions of communion among neighboring churches that has gradually been adapted over time to reflect the present situation of the universal Church.

However, hypothetically speaking, under a completely new system of electing a pope, it is possible that women could also be involved.

Finally, it is not quite correct to say that the pope is also bishop of Rome. It is more correct to say that the bishop of Rome is, by that very fact, the pope. There could not be a pope who is not bishop of Rome, although there have been situations when he was not resident in the city. This unique status of the Diocese of Rome has meant that it is not formally an archdiocese.

http://www.zenit.org/en/articles/women-as-cardinals

I recall this subject coming up before I escaped the Novus Ordo.  This has already been discussed and, if memory serves, the Conciliar church does not believe there is any real impediment to women cardinals since the creation of cardinals and their status is purely a construct of canon law and such can be changed.  The decision, at the time, was that the Church was just not yet ready for a woman cardinal.

Of course, that was before some Conciliar bishops are seriously raising the spectre of women's ordination.  Perhaps the time is right for women cardinals (and priestesses) in the Conciliar church.  Would such an event force the hand of Bishop Fellay?  (Probably not.)

Here is an explanation from Fr Mcnamara about why women cannot become cardinals...

Whoever Fr. McNamara is, it is clear that, in the Conciliar church, it is more correct to say that women cannot become cardinals...until they can.  Nothing is permanent in that sect.