Why was Peter's experience at Cornelius essential to Paul's defense and the spread of Christianity?
Peter's Cornelius experience was essential because it opened his eyes that God could save Gentiles by simple faith, without their becoming Jewish proselytes. When Paul was called to Jerusalem to answer opposition, Peter defended him by recalling this. Without that testimony, Paul would not have been released and Christianity would not have spread.
Les explains that Peter came to Paul's defense at Jerusalem and remembered how God had sent him to the house of Cornelius. That experience opened Peter's eyes to the fact that God could save Gentiles without their becoming proselytes of Judaism. In Acts 15, after there had been an uproar and Jewish jealousy over their relationship with Jehovah, the multitude kept silence and listened to Barnabas and Paul declare what miracles and wonders God had wrought among the Gentiles. Les often says God does everything sovereignly: had Peter not had that eye-opening experience at Cornelius, Paul would never have gotten off the hook, and Christianity would never have gotten off the ground. God opened Peter's eyes twelve years earlier to the fact that Gentiles could be saved by simply believing.