Why did Peter stay focused on Jews instead of going to the Gentiles after his experience at Cornelius?
Peter remained focused on the Jews because he understood his ministry was to be confined to the circumcision, not the Gentiles. In Galatians chapter 2, he and the Jerusalem leaders agreed that Paul was to go to the Gentiles, while Peter stayed with Israel even after Cornelius.
Les teaches that after Peter came back to Jerusalem from his experience at Cornelius, he still was not going out to the Gentiles. As shown in Galatians chapter 2, Peter understood he was not supposed to; he was to confine his ministry to the Jew, to the circumcision, and they agreed that Paul was to go to the Gentiles. Les stresses that Acts is a transitional book, and chapter 11 shows the transition kicking into a little higher gear. So far it had been all Jewish, and even the scattered believers in Acts 11:19 preached the word to none but Jews only.