When I was master of ceremonies at our Cathedral from 1985 to 1991, the late Bishop Raymond Lessard only wanted to wash six feet of either men or women. Of course, it is quite common for bishops around the world to wash the feet of 12 men and women.
So I asked Bishop Lessard, why just six?
He said, using 12 is symbolic of the 12 Apostles, the first to receive the fullness of Holy Orders, the first priests and bishops of the Church. Jesus, the High Priest, teaches them that their ministry is not just cultic but also practical--they are not to fear "ritual impurity" as the Jewish priests did. Catholic bishops, priests and deacons are to get their hands dirty ministering to the sick, helping the poor and offering the Word and Sacraments of the Church to those in need of God's salvation. They are to worship God in spirit and truth.
But washing six feet of men or women is a sign that all God's people who in one degree or another share in the baptismal priesthood of the faithful, are not to be "just Sunday" or cultic Catholics but should also get their hands dirty in the world doing the work of Christ especially in their Christian homes, the Church in miniature, and in the public square.
That is why I wash the feet of only six people of either gender as s sign that all of us must imitate Christ in assisting the poor, sick, and needy as well as celebrate Mass each Sunday and Holy Day of Obligation, go the Confession regularly, get married in the Church, discern a vocation to the ordained life or religious life, get anointed when sick or dying and live their sacraments of Baptism, Confirmation and Holy Eucharist. It's quite simple when you think about it.