Paul continues to uphold his authority by describing those events which support it, specifically his meetings with the Jerusalem church leaders. His purpose is to counteract the smear campaign conducted against him by the false teachers. He proclaims that although he was not dependent on anyone but God for his commission and the message he preached, he preached the same gospel the other apostles did, with their knowledge and approval. This is also demonstrated by Peter’s reaction to the incident in which Paul chastised him for his duplicitous behavior when fellowshipping with Gentile believers at Antioch.
Paul’s main concern, however, was not self-justification and pride. He was concerned for the truth, the unity of the church, for the edification of believers and the salvation of the lost. He wanted to uphold the truth of the gospel which frees the Gentile believers (and all believers) from the requirements of the law. He also desired to see that all believers held equal status in the Church and before the Lord. This he does by proclaiming the central truths of the Christian faith: all believers are incapable of keeping the Law but all believers are in Christ so all receive the benefits of His atoning sacrifice. Essentially then, no amount of keeping of any laws by humans can bring them closer to God. Christ keeps the law for us and through us.
A legalist thinks and teaches otherwise. You may be such a person if you think Christianity is at heart a set of rules and moral laws that must be followed by everyone and if you try enforce those rules on others. You may be a legalist if you condemn those who do not agree with your lists of rules or who disagree with your pet theological doctrines. The gospel is about love and mercy not anger and hatred. We should feel sad for those who reject our message for they face eternal chaos and emptiness.