Why does Jerry compare himself to the Apostle Peter? What makes Jerry think of this comparison?

Jerry's comparison of himself to the Apostle Peter is an allusion to the Biblical account of when Peter, after asserting to Jesus that he will remain forever faithful to Him, denies him three times. In the hours before his suffering and death, Jesus gathers his disciples together and warns them about what is to come. Jesus says, "This very night you will all fall away on account of me" (Mt. 26:31, NIV), and Peter responds, "Even if all fall away on account of you, I never will" (Mt. 26:33, NIV). A short time later, after Jesus is arrested, Peter is sitting out in the courtyard, when a woman recognizes him as a follower of Jesus. Peter, afraid, vehemently denies knowing Jesus three times, despite what he has said before. After his third denial, a cock crows, and Peter, realizing what he has done, weeps bitterly at his own weakness.

When Jerry takes a beating in football and the coach bellows at him contemptuously, spitting on him in the process, Jerry does not express the anger he is feeling, telling the coach only, "I'm all right", instead of protesting about his treatment like he would like to. Jerry compares himself to Peter because he considers himself a coward, "thinking one thing and saying another, planning one thing and doing another - he (has) been Peter a thousand times and a thousand cocks (have) crowed in his lifetime" (Chapter 1).