Why did the Corinthians accuse Paul of not having the same authority as Peter, James, and John?
The Corinthians accused him because Peter, James, and John had been with Christ for three years, so they seemed to have an authority Paul lacked. Paul had to defend his God-ordained apostleship to the Gentiles and show that he also had direct contact with Christ, though not by walking with Him in Palestine.
Les explains that Paul had to constantly remind not only the Corinthians but also you and I that he was the God-ordained apostle of the Gentiles. The Corinthians, evidently a mixture of some Jews but still mostly Gentiles, were bombarding him with accusations that he did not have the authority Peter, James, and John had, because they had been with Christ for three years. Paul's defense was that he also had direct contact with Christ, not in the same way as the Twelve walking up and down the dusty roads of Palestine, but the Lord appeared to him over and over, especially to encourage him amid sufferings and disappointments. In II Corinthians 11:22 he asks whether they are Hebrews, Israelites, or the seed of Abraham, and answers, "So am I," showing that genealogically they had nothing over him.
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Why did the Corinthians accuse Paul of lacking authority?
Paul had to defend his apostleship because the Corinthians accused him of lacking the authority that Peter, James, and John had, since they had been with Christ for three years.