F.F. Bruce attempts to recreate the arguments against Paul being advanced by the Galatians. From The Epistle to the Galatians by F. F. Bruce:

“The Jerusalem leaders are the only persons with authority to say what the true gospel is, and this authority they received direct from Christ. Paul has no comparable authority: any commission he exercises was derived by him from the Jerusalem leaders, and if he differs from them on the content or implications of the gospel, he is acting and teaching quite arbitrarily. In fact,” they may have added, “Paul went up to Jerusalem shortly after his conversion and spent some time with the apostles there. They instructed him in the first principles of the gospel and, seeing that he was a man of uncommon intellect, magnanimously wiped out from their minds his record as a persecutor and authorized him to preach to others the gospel which he had learned from them. But when he left Jerusalem for Syria and Cilicia he began to adapt the gospel to make it palatable to Gentiles. The Jerusalem leaders practised circumcision and observed the law and the customs, but Paul struck out on a line of his own, omitting circumcision and other ancient observances from the message he preached, and thus he betrayed his ancestral heritage. This law-free gospel has no authority but his own; he certainly did not receive it from the apostles, who disapproved of his course of action. Their disapproval was publicly shown on one occasion at Antioch, when there was a direct confrontation between Peter and him on the necessity of maintaining the Jewish food-laws.” (Galatians, 26).