Adam Clarke on Galatians 2:5

To whom we gave place by subjection - So fully satisfied was he with his Divine call, and that he had in preaching among the Gentiles acted in strict conformity to it, that he did not submit in the least to the opinion of those Judaizing teachers; and therefore he continued to insist on the exemption of the Gentiles from the necessity of submitting to Jewish rites; that the truth of the Gospel - this grand doctrine, that the Gentiles are admitted by the Gospel of Christ to be fellow-heirs with the Jews, might continue; and thus the same doctrine is continued with you Gentiles.