The disciples evidently had no problem in understanding the designation “Son of Man” as Jesus’ personal reference to himself (cf. Mark 8:27). The usage here reminds the reader of Jesus’ humble earthly service (8:20; 10:23; 12:8, 32; 13:37, 41).
However, Peter’s Christological insight should not be construed as a sudden flash of insight, but was fundamentally grounded in his observation of Jesus’ performance in word and deed. As a matter of fact, Jesus’ entire ministry was performatively God’s revelation concerning the mystery associated with his person.