Why were some doctrines kept from Peter and the eleven?
God kept certain doctrines of grace, associated with the Church, secret from Peter and the eleven because He is sovereign. The context explains that God held these things from them, and they could not have heard or comprehended them, because God's sovereign will determined that these mysteries would be revealed to Saul (Paul) later.
Les explains that after Saul's conversion in Acts 9, God would take him into the desert for three years and reveal to him all the doctrines of grace associated with the Church—things that had been kept secret. In Acts 9 Saul is saved as the pattern, the chief of sinners at the head of the line; then in Acts 10 a house full of Gentiles is saved. Les notes that if Cornelius had been saved in chapter 8, the whole plan would fall apart. He stresses Deuteronomy 29 as fundamental to understanding why God held some things from Peter and the eleven, and why they could not have heard and comprehended them: because God is sovereign.