Why does Peter's Acts 2 sermon not fit Paul's doctrine?
Peter's Acts 2 sermon does not fit Paul's doctrine because Peter charged Israel with killing Jesus and declared Him Lord and Christ, while Paul's theme is that Christ gave Himself and died for us while we were yet sinners. It was not supposed to fit, since God had not yet revealed Paul's message; it remained a secret in God's mind.
Les teaches that you should set Paul's writings over on one side and look at the vast difference. You cannot mix them, but keep them separate, and then your Bible opens up beautifully. Paul writes in Galatians that grace and peace come from God the Father and the Lord Jesus Christ, who gave Himself for our sins that He might deliver us from this present evil world according to the will of God. Paul's theme is that He commended His love toward us, in that while we were yet sinners, He died for us. Peter, however, says, "You killed Him." The difference is as different as daylight and dark. Peter's sermon just doesn't fit Paul's doctrine at all, and it wasn't supposed to. God hadn't revealed Paul's message yet; it was still a secret kept in the mind of God. In Acts 2:36, Peter tells the house of Israel to know assuredly that God hath made that same Jesus, whom they crucified, both Lord and Christ.