objectivetruth-
Jesus is not the Jewish Messiah. Peter could not continue in Judaism and yet at the same time believe Jesus is the Messiah.
For one thing, the Jewish Messiah has two human parents, and does not become a sacrifice to cover other's sins as the Jewish religion teaches no-one else can die for your sins.
Judaism also teaches that God does not want or accept human sacrifice.
The Jewish Messiah will not be a redeemer for people's sins.
But Jesus said he was there to die for his followers sins and would be sacrificed. A follower of Judaism would not have accepted Jesus as Messiah.
I am Jewish by birth as are all of my blood relatives. But while I was a witness, therefore a' Christian" my relatives did not consider me to be "Jewish" because I was a "Christian"!
Peter could not have accepted and believed that Jesus would die for his (and other's sins) if he really believed in Judaism.
Also, the Jewish Messiah is not "the son of God". But Jesus taught that he was. Peter beleived that.