The basic story of the washing of the disciples’ feet doesn’t need to include the conversation between St. Peter and Jesus.
John 13:2b-5,12-16
So, during supper, fully aware that the Father had put everything into his power and that he had come from God and was returning to God, he rose from supper and took off his outer garments. He took a towel and tied it around his waist. Then he poured water into a basin and began to wash the disciples’ feetd and dry them with the towel around his waist…
So when he had washed their feet [and] put his garments back on and reclined at table again, he said to them, “Do you realize what I have done for you? You call me ‘teacher’ and ‘master,’ and rightly so, for indeed I am.h If I, therefore, the master and teacher, have washed your feet, you ought to wash one another’s feet. I have given you a model to follow, so that as I have done for you, you should also do. Amen, amen, I say to you, no slave is greater than his master nor any messenger greater than the one who sent him.
For whatever reason, John included the discussion between St. Peter and Jesus.
John 13:6-10
He came to Simon Peter, who said to him, “Master, are you going to wash my feet?” Jesus answered and said to him, “What I am doing, you do not understand now, but you will understand later.” Peter said to him, “You will never wash my feet.” Jesus answered him, “Unless I wash you, you will have no inheritance with me.” Simon Peter said to him, “Master, then not only my feet, but my hands and head as well.” Jesus said to him, “Whoever has bathed has no need except to have his feet washed, for he is clean all over; so you are clean, but not all.”
Here is what
Haydock had to write about it:
Ver. 10. He that is washed, &c. The feet are always apt to contract some dust or dirt; and in the mystical sense, he that is washed by the sacraments of baptism, or penance, from greater sins, must still endeavour to cleanse, and purify his affections from lesser failings of human frailty. And you, my apostles, are clean from greater offences, but not all of you, meaning the traitor Judas. (Witham) — It is impossible that the extremities of the soul (if we may be allowed the expression) should not, as long as we tread upon this earth, receive some stain or other; although in the opinion of men, the soul appear just. Many indeed after baptism, are covered with the dust of sin, even to the head, but those who are disciples indeed, need only to wash their feet. (Origen, tract. 32. in Joan.) — The foulness of the feet, when the rest is clean, signifies the earthly affections, and remains of former sins remitted, which are to be cleansed by devout acts of charity and humility. (St. Ambrose, lib. iii. de Sacram. chap. 1; St. Bernard, de cæn. Dom. ser. 1.) — Though his disciples were clean, still he washed their feet, comformably to that of the Apocalypse, chap. xxii. “He that is clean, let him be cleansed still.” (Origen, tract. 32. in Joan.)