Why doesn't Les base his teaching on Peter's words about baptism?
Peter's words about baptism are not the basis of the teaching because Peter was the apostle of the Jew, while Paul is the apostle of the Gentile. Paul separates himself by the inspiration of the Holy Spirit in Galatians chapter 1, verse 11, so Gentile teaching follows Paul.
Les explains that he has received letters asking why he does not go by what Peter says about baptism. His answer is that Peter was the apostle of the Jew, and Paul is the apostle of the Gentile. Paul separates himself by the inspiration of the Holy Spirit in Galatians chapter 1, beginning in verse 11. That distinction means Gentile believers follow Paul's apostolic authority rather than Peter's baptismal instructions. The context also shows Peter required Judas's replacement to be someone converted from John's baptism, a follower of Jesus through His three-year ministry, a witness of His resurrection, and a hearer of His 40 days of teaching—qualifications Saul of Tarsus did not meet.
But I certify you, brethren, that the gospel which was preached of me is not after man.
More Questions
Why does Les not always go by what Peter says?
Les does not simply follow everything Peter says about baptism and similar practices because Paul, not Peter, is the apostle to the Gentiles, and in Galatians 1:11 Paul separates himself by the inspiration of the Holy Spirit.