Typically when considering the sacraments, I think about what they effect and not so much about what they signify, yet these are closely related. Most definitions of sacrament will somehow include sign, whether be "an efficacious sign of grace" or "an outward sign instituted by Christ for giving grace" (Baltimore Catechism) or "a sign of a sacred thing, with determinate words and a determinate matter" (St Thomas).
Lately I've been thinking about the question, "Why not women priests?" I'm thinking more and more that the answer is that a woman (as woman) is not a sufficient sign of Christ the Priest. It seems that it has to be on account of the sign. As far as offering sacrifice (which is the chief act of a priest), this is not something only men do. We are all called to be "a nation of priests" and "offer sacrifice" in all of our thoughts, words, and actions. Yet when people talk about the capacity to become priests, they are referring to the sacramental priesthood, the priesthood which is a sign of the priesthood of Christ.
Now I'm talking about signs a lot and some might think, "If it's just a sign, then doesn't that mean it doesn't really matter?" The answer is no, it really does matter. Think about baptism: the washing with water signifies the washing away of sins--no water, no sacrament. But all the other liquids may complain, "If it's just a sign, can't you use beer or coffee to baptize someone just as well?" Christ, in his wisdom, instituted the sacraments with determinate things and with determinate words so that they might have determinate effects. The tendency to attend only to the effect of the sacrament and not to the sign might be a result of a kind of utilitarian mindset, but without attending to the sign we cannot understand the reality effected by means of the sacrament.
Marriage is another example of a sacramental sign. Why can't two men marry each other in a church? (at all really, but especially not sacramentally.) Because marriage is primarily a sign of the union between Christ and the Church, a union which requires a both diversity in kind and a total self-giving of the one to the other. You do not have this in two men. Perhaps two men can have the holiest of friendships and can even spend a whole of service together (these aren't typically the men that seek such a union...), yet their friendship does not sufficiently signify the union of Christ and the Church, a union which is signified by bride and bridegroom, male and female.
Another example intrigues me in the sacrament of Confirmation. At the Council of Trent, it was declared "If
anyone says that the ordinary minister of holy confirmation is not the bishop alone,
but any simple priest, let him be anathema." I always thoughts this was an odd canon since it is only about an ordinary minister of a sacrament. Simple priests can administer confirmation, yet the Church declares that bishops are the only ordinary minister. Why? Because the bishop more perfectly signifies the one who sends the Holy Spirit. I will have to read more on this, but St. Ignatius of Antioch (2nd century bishop in Syria) often compares the bishop to God the Father, priests to Christ or the company of Apostles, and deacons to the ministry of the Apostles. Both the Father and the Son send the Holy Spirit, thus both the bishop and the priest have this capacity, and yet all the Son has he has from the Father (including, if I am not mistaken, that the Holy Spirit proceeds from him), thus it is proper that the bishop be the ordinary minister of the sacrament by which the Holy Spirit is confirmed in souls. (A note: these are just top-of-head thoughts, if I say something that sounds heretical, check the catechism and disregard what I said as needed)
After considering the sacramental priesthood to some extent, there is also the question of other ministers at Mass. Many argue that these should be male whenever possible, citing what appears to be the meaning of Canon Law but also arguing that the other ministries are in some way a participation in the priesthood. There is certainly more leeway here, since these are ministers (besides the priest and deacon) do not receive a sacrament, yet the principle of a significant sign should still apply. Thus, when the Epistles of St Paul or any of the Apostles is read, it does seem fitting that a male should read these so as to signify the Apostle better. Another example of a sign beyond the sacraments: I know a priest who always has the gifts brought up from the congregation (although this is not required) since this better signifies the contribution of man in the divine sacrifice.
Must go to class. Signs--very important.