Today I was struck by Luke’s juxtaposition of this question. I never before realized that Luke provided parallel explorations of the question. Consider first Luke 9:7-9 (NLT):
When Herod Antipas, the ruler of Galilee, heard about everything Jesus was doing, he was puzzled. Some were saying that John the Baptist had been raised from the dead. Others thought Jesus was Elijah or one of the other prophets risen from the dead. “I beheaded John,” Herod said, “so who is this man about whom I hear such stories?” And he kept trying to see him.
While it is odd that Herod would come to bare upon the narrative, it is not unreasonable since Jesus had just healed the roman officer’s servant in Luke 7. But the real reason seems to be to contrast Herod’s wisdom as a ruler with the wisdom of his disciples. There is an apparent chronological gap (“one day…”) before reaching Luke 9:18-22 but the symmetry is clear:
One day Jesus left the crowds to pray alone. Only his disciples were with him, and he asked them, “Who do people say I am?” “Well,” they replied, “some say John the Baptist, some say Elijah, and others say you are one of the other ancient prophets risen from the dead.” Then he asked them, “But who do you say I am?” Peter replied, “You are the Messiah sent from God!” Jesus warned his disciples not to tell anyone who he was. “The Son of Man[e] must suffer many terrible things,” he said. “He will be rejected by the elders, the leading priests, and the teachers of religious law. He will be killed, but on the third day he will be raised from the dead.”
Read the whole chapter of Luke 9 (NLT).