I dunno, maybe because the rubrics of the liturgy specify viri ("men", as in "adult male humans," not homines, human beings of unspecified gender), and when the chief executive ignores the rulebook and does his own thing (Barack Hussein Obama, call your office), it sets a bad example?
The persons whose feet are being washed are supposed to represent the Apostles, not generic "people in need". The Apostles were all men, and the fact that the Apostles were all men is usually cited as part of the rationale for an all-male priesthood.
Until fairly recently, the foot washing was only done by the bishops to 12 priests at the bishop’s Chrism mass. This was to symbolize humility.
After Vatican II, the practice was extended to parishes. Probably because of the possibility of scandal (Father washing the feet of some attractive woman, for example), in 1980 it was provided that the parish-level washees, so to speak, should be viri, that is, men.
So this is not an ancient tradition and the restriction to males is fairly recent and was purely practical, not symbolic or laden with meaning. A person who has his or her feet washed is not thereby considered a successor to the Apostles or a candidate for the priesthood, but simply a humble person to whom a person more important in worldly terms is deferring and showing that what is really important is to use one’s abilities and position to serve others and not to lord it over them. It has nothing to do with ordination.
I don't agree. Jesus specifically said that the apostles were to do this for others; He didn't say just for other men. This was to show that they are to be servants, not masters.
This wasn't the same as Jesus sending the Apostles out on the Great Commission, to preach the Gospel, and consecrate the bread and wine to become His Body and Blood. THAT was the institution of the priesthood, and for that he did choose just men.
You sound remarkably like a Pharisee