Why did the Corinthians think Peter, James, and John had more authority than Paul?
The Corinthians assumed Peter, James, and John had greater authority because they had been with Christ for three years during His earthly ministry. Paul had not walked with Jesus in that way, so they questioned his apostleship. He counters by showing he too had direct contact with Christ and equal covenant lineage.
Les explains that Paul constantly had to remind the Corinthians, and us, that he was the God-ordained apostle of the Gentiles. The Corinthians, mostly Gentiles with some Jews, were bombarding him with accusations that he did not have the authority Peter, James, and John had, because those men had been with Christ for three years. Les teaches that Paul shows he also had direct contact with Christ, not by walking the dusty roads of Palestine as the Twelve did, but because the Lord appeared to him over and over, especially to encourage him amid sufferings and disappointments. In II Corinthians 11:22, Paul argues that the Twelve had nothing over him: if they were Hebrews, Israelites, and the seed of Abraham, so was he, and he also was a minister of Christ.