Let's look at the theology here:
The foot-washing ceremony at the Mass of the Lord's Supper on Holy Thursday is a sign of the total humility which the priest is supposed to have. Although he is in charge of his parish and holds a place of honor and respect, he is must not let it "get to his head". He is a servant of God and His people. When Jesus washed the feet of His disciples he modeled a bit of the kenosis, self-sacrificing love, which is required of the priest. It was a prelude to the ultimate self-sacrificing love which Jesus was about to perform the very next day on the Cross. Jesus often mentioned in the Gospels about how the priests of his time abused their power for their own gain and gave little concern for God or their flock. The priesthood which Jesus was establishing at the Last Supper was not to be that way. These priests were to always realize the gift of the priesthood was always for the service of God and others. Priests are reminded of this in a special way on Holy Thursday as the wash the feet of some of their parishioners. They are in charge, but they are not to use their position for their own gain or to get what they want. They are to always serve.
There are some who think that everyone in the parish or everyone who performs a ministry in the parish should wash feet during this ceremony, but that is inappropriate. It is the role of the priest. To have everyone wash feet is to deny the special role that the priest holds and in the end accomplishes the opposite of what the ceremony is meant to symbolize because the priest fails to humble himself. Every priest stands in the person of Christ at Mass. God comes upon and uses the priest in a way that He uses no other human being. In washing feet, the priest acknowledges that he is called to model himself after Christ in a special way.
Hand-washing in the Jewish culture was a purification rite. That is why the priest washes his hands before offering the bread and wine at Mass. As he washes his hands he says, "Lord, wash me of my iniquities and cleanse me of my sins". It is a reminder of his own unworthiness to offer this sacrifice and a prayer asking for forgiveness for his own sins. There is, however, another prominent handwashing scene in the Holy Week story. Pontius Pilate washed his hands when he handed Jesus over to be crucified. In this case, Pilate was doing the opposite of what Jesus modeled. Pilate washed his hands to symbolize that even though he was in charge, he didn't want to be blamed for anything bad that would happen. He was afraid that a riot would break out during the busiest week in Jerusalem and he would be in trouble with Caesar. Pilate was looking out for his own interests, and he didn't care if an innocent man had to die. He was covering himself.
So, who do you think should be emulated? Jesus or Pontius Pilate?