Peter was close to Jesus and saw Jesus do many wonderful things. Perhaps because he was fearful, Peter began to deny Jesus around the time when Jesus would have liked Peter’s support the most. We are not supposed to be close to Jesus only during the easy times, but during the hard times too. There are people in the world at this moment who are suffering and dying because they willingly show that they are followers of Jesus.
Jesus’ relationship with earthly rulers is interesting. Jesus himself is the Son of God and true King. Jesus encouraged taxes to be paid, and surrendered himself before the Roman governor. But he always told the truth, and did not seem to be at all concerned about what he said when he was before the high priest.