John 18:1-11 presents Jesus leaving Jerusalem, where he had taught his disciples in the upper room and had prayed for them. He goes across the Kidron Valley to an olive grove, where John describes his arrest. Jesus’ choice of a route and destination was a self-conscious choice by the King. As 2 Samuel 15 indicates, this was the route that King David had followed, approximately 1,000 years earlier. Like David, whose son had turned against him, Jesus was betrayed by one of the men in his inner circle.
But notice the contrasts. David was fleeing for his life. Jesus was crossing the Kidron in order to be arrested and go to his death. David fled to retain his throne. Jesus, who already was truly King, was going to his betrayal, suffering, and death in order to ascend to a more magnificent, triumphant aspect of his kingship.
Herman Ridderbos comments:
“Jesus is not departing as the victim of Judas’s betrayal and the superior might of his enemies. He has the power to lay down his life before taking it up again, and no one takes it from him (10:18). What he does and suffers he does and suffers out of love for and obedience to the Father. (cf. 14:21). But his suffering is not for that reason any less real, and Jesus does not pass though it as if he were inviolable. The ‘cup’ symbolizes, rather, the bitterness of the suffering and death he must endure (cf. Mt. 26:39 par.). It is the surrender of his life, which he must give for his own (17:19) and for the life of the world (6:51) as the Lamb of God who thus carries away the world’s sin. . . . Jesus’ power consists in his obedience to do ‘as the Father has commanded’ him (14:31) to the bitter end.” (The Gospel of John: A Theological Commentary, p. 578)
(Preparing for the Wednesday evening Bible study and prayer time at Trinity Presbyterian Church, OPC)