Apostle Paul begins the letter by affirming his authority in Christ, and then continues to remark that he is surprised to hear that the Galatians have already strayed from believing in the true Gospel that Paul originally taught them and instead listening to other teachings that are contrary.
The question to answer for this post is, why should the Galatians have trusted Paul over these other false apostles?
Paul affirms his authority in two ways, which both rest on the idea that his message and authority come from Christ rather than man. Of course, anyone can make this claim without proof, so Paul is clear to explain why he should be trusted. He does this by claiming that the false teachers who have taught them 1) they aim to please man 2) they are contrary to Paul's original teaching.
First, these false teachers likely preached messages that pleased the fleshly interests of the listeners (2 Timothy 4:3) instead of the sanctifying holy word from God. This was for their own gain. The true Gospel that Paul preached instead serves not to please, but to convict, and to express the good news of Jesus in the reality of our condemned nature. If Paul had his own interests in mind, he would not be preaching something so offensive and radical for that wins no favor among those who don't believe.
Secondly, Paul claims that his message is directly from Christ himself instead of man or even an angel. He proves this with his conversion testimony of going from persecuting Christians to having the Son revealed to him and being called to Arabia on his own to reflect on the revelation. It is from this testimony and also the alignment/agreement of his understanding with the original Apostles that give credible proof to his own teachings.