Paul testifies to the grace of God in regard to his election. He had been set apart before he was born, and called by God's grace to serve Christ. He is writing to the church in Galatia to bring them back to the freedom we have in Christ. And he needed to establish his bonafides as a legitimate servant of God. He needed to pull rank over the people who had come into their church and caused confusion, even leading them away from faith in Jesus.
But he doesn't do this apart from testifying to God's grace. That's the beauty of a true Christian witness. We don't have to prove ourselves to be better than anyone else. We can point to God's grace to us: his undeserved kindness, love and goodness toward us - in spite of the sinful, silly, dumb, hair-brained, and dangerous things we have done.