Why was Peter still appealing to Israel using Old Testament prophecy?
Peter still appealed to Israel through Old Testament prophecy because he did not yet understand the Church Age or the Body being called out. He was holding to the Old Covenant program, expecting Israel to accept Jesus as Messiah, after which the tribulation would unroll and God would send Jesus.
Les explains that Peter was still appealing to Israel on the basis of Old Testament prophecy because, as yet, he did not understand the Church Age—God calling out the Body, a people for His name. Peter kept sticking to the Old Testament prophets and the Old Covenant program. He expected Israel to accept that Jesus was their Messiah; then the tribulation would unroll and God would send Jesus. The first part of Acts is Peter and the nation of Israel, until Israel continues to reject and a departure comes—Saul’s conversion and Peter going to Cornelius—so Israel goes off the scene and Gentiles come in under grace.