It is quite unlikely that faith in God would produce arrogance or overconfidence. On the other hand, faith produces hope, trust, gratitude, purpose, compassion, and resilience. Different individuals may have different interpretations of faith, which may lead to variations in the attitudes they develop as a result.
We must remember that Peter was just a fisherman, and probably had received little formal education. He was one of the three who witnessed the transfiguration of Jesus: in other words, he saw God in His glory, though only fleetingly. Unlike many educated people of today, he did not gloat about this privilege God had blessed him with. Many of us take pride in knowing personally the higher-ups, and it is in that very attitude that arrogance begins.
Peter lost his faith after taking a few steps on the water, and he failed again in his faith when he denied even knowing Jesus. So much so that Jesus, after His resurrection, reminded Peter of this over a charcoal fire on the beach. Peter is often portrayed in the Gospel accounts as impulsive and outspoken, yet his character can equally be seen as one of great passion and loyalty. Despite his moments of failure, Peter also displayed humility and a willingness to learn from his mistakes, making him a complex and multifaceted character.
When true faith loses its focus on God, it shifts instead to fanaticism, and such people always set their own standards, and find others wanting by them.