Origen — as excerpted in the Catena Aurea on John 13:6-11

“(t. xxxii.) Or our Lord insinuates that this is a mystery. By washing and wiping, He made beautiful the feet of those who were to preach glad tidings, (Is. 52:7.) and to walk on that way of which He tells them, I am the way. (infr. 14:6) Jesus laid aside His garments that He might make their clean feet still cleaner, or that He might receive the uncleanness of their feet unto His own body, by the towel with which alone He was girded: for He hath borne our griefs. Observe too, He chose for washing His disciples’ feet the very time that the devil had put it into the heart of Judas to betray Him, and the dispensation for mankind was about to take place. Before this the time was not come for washing their feet. And who would have washed their feet in the interval between this and the Passion? During the Passion, there was no other Jesus to do it. And after it the Holy Ghost came upon them, by which time they should already have had their feet washed. This mystery, our Lord says to Peter, is too great for thee to understand now, but thou shalt know it hereafter when thou art enlightened.”