Luke omitted Jesus' prediction of the church (Matt. 16:17-19), Peter's rebuke of Jesus (Matt. 16:22; Mark 8:32), and Jesus' counter-rebuke of Peter (Matt. 16:23; Mark 8:33). These omissions enabled him to stress Jesus' prediction of His sufferings and His call to the disciples to take up their cross and follow Him. The fate of Jesus is primary in this pericope.
Evidently Jesus urged the disciples not to publicize His true identity because this would have resulted in unnecessary pressure from the Jewish multitudes. He would publicly proclaim His messiahship at the proper time, namely in the Triumphal Entry. Next Jesus gave His first clear prediction of His passion (cf. 2:35; 5:35). In view of what Jesus needed to teach the disciples, they needed to hear that rejection, death, and resurrection lay ahead for Him.
Jesus' use of the divine title "Son of Man"(v. 22) supports the fact that Peter recognized Jesus' deity. It was appropriate to use this title when speaking of His rejection since the Old Testament predicted the Son of Man's glorious reign (Dan. 7:13-14). The disciples had seen Jesus raise two people from the dead, the widow of Nain's son and Jairus' daughter. Their failure to understand that Jesus would rise from the dead was, therefore, not due to its actual impossibility but to its improbability since Jesus was the Son of Man.