Jesus was taken to suffer severely.I think Peter by confessing that he will stay with Jesus till the end never thought of such a torture.So perharps when he saw the much suffering he could not withstand,he became so afraid that he thought if he identifies with Jesus he would undergo the same torture.Also it happen so that what Jesus had prophesied that before the rooster crows Peter was to deny him three times come true.

  Knowing that Jesus is the Truth and the way...,and given the ills and the corruption that people do in order to end a living,most people are afraid of the truth.So they turn to be afraid of identifying with Jesus.