When in depression, one can understand Isaiah's "I have toiled in vain, I have exhausted myself for nothing." (Isaiah 49:4) in the second of four songs about the servant of Yahweh. Isaiah's sense of disappointment arose from the many difficulties he faced in proclaiming God's message, which, essentially, was one on the necessity of conversion to God, of a moral return. The purpose of this conversion was that "my salvation may reach to the ends of the earth." (Isaiah 49:6). However, despite his frustration, Isaiah was aware of the honour given him in being chosen to proclaim this message, that "God was my strength" (49:5).
In John's Gospel, Jesus too chose from amongst the disciples around Him. He chose to pick out Judas for a special token of intimacy by offering him a morsel of food. Unfortunately, the evil at work in Judas' heart made him reject Jesus' love. Despite that the offer of intimacy - a place to rest on His breast - to the Beloved Disciple, was accepted positively. The Beloved Disciple here stands for all disciples ever after who accept Jesus' love and choose to be close to Him.
As for Peter, his response to Jesus' words about His departure and His glorification was that of a willing follower even to the end of his days. Jesus warned him of his weakness in denying him initially, but his later steadfast following of Jesus with his whole life manifested the power of God.
Lord, we are all chosen though in different ways.