John 13 begins the final-night teaching with Jesus washing his disciples' feet, then moves through Judas' betrayal and departure to Jesus' command that the disciples love one another as he has loved them, before ending with the prediction of Peter's denial.
Knowing that his hour has come, Jesus performs the role of a servant and washes the disciples' feet. Peter resists, then overcorrects, and Jesus explains both the deeper necessity of receiving what he does and the example the disciples are expected to follow in their relationships with one another.
The atmosphere then darkens as Jesus identifies the betrayer and Judas leaves. Only after the departure does Jesus speak of the Son of Man being glorified and give the new commandment. Peter responds to the announcement of Jesus' departure with confidence about his own loyalty, and the chapter ends with Jesus predicting that Peter will deny him three times.
The foot washing becomes both a sign of Jesus' self-giving posture and a model of the kind of service expected among his followers.
Jesus becomes troubled, identifies the betrayer through the shared meal, and Judas leaves into the night.
With betrayal in motion, Jesus speaks of glorification and commands the disciples to love one another according to the pattern of his love.
Peter insists he will lay down his life for Jesus, but Jesus answers with a prediction of three denials before the rooster crows.
Jesus' awareness of where he comes from and where he is going is placed beside the deliberately lowly act of washing feet.
The new commandment is not abstract affection; its stated pattern is Jesus' own love and its public effect is recognition of the disciples as his followers.
Peter's promise to lay down his life is immediately answered by a prediction that exposes how much his loyalty will be tested.
The command to love one another is repeated and deepened through the language of laying down one's life for friends.
The prediction about Peter is fulfilled during Jesus' arrest and hearing.