Why does Paul keep defending his apostleship in all his letters?
Paul kept defending his apostleship because wherever he ministered he faced constant slurs that he was an imposter, a renegade Jew, and not a true representative of Judaism. To counter that opposition and the divisions it fueled, he had to affirm repeatedly that he was God's man for the hour.
Les points out that throughout Paul's letters he is always defending his apostleship, and it stands to reason. In Paul's early ministry he went first to the Jew, to the synagogue where he might get a halfway civil hearing, and when the Jews rejected the message he went out into the Gentile area, the marketplace, and wherever else. But wherever he went there was that constant slur on the man that he was an imposter, not a true representative of Judaism, a renegade Jew. So he always has to come back and defend the fact that he is God's man for the hour. In Corinth specifically, Paul made plain the Corinthians were still carnal, not a spiritual church like Ephesus or Philippi, but a church beset with problems, including divisions where some said they followed Paul, some Apollos, some Peter, and some even Christ. As Paul addressed those divisions, he had to defend his apostleship. Beginning in verse 9, after straightening up some problems, he comes to these carnal Corinthians, who were nevertheless still co-laborers with the Apostle, which puts believers in the same place as co-laborers together to bring to fruition the eternal will of God.