I did not receive it from any man, nor was I taught it; rather, I received it by revelation from Jesus Christ.
False teachers have come into the churches of Galatia after Paul left and undermined His teaching. Because of this, Paul is in the unenviable position of defending His credentials as an apostle in order to defend his message.
He doesn’t do this to promote himself, but rather to show that His teaching comes directly from Jesus. Whereas, these false teachers do not have the authority of an apostle as Paul does.
Paul’s concern is for the spiritual health of the churches he worked so hard to establish. He fears they will fall from the grace of God into a system of legalism being taught by others. He only presents his credentials to underscore the truth of what he taught these Christians, so they won't be led into error.
Paul’s defense of his authority as an apostle of Jesus indicates something of what these false teachers must have been saying about him.
But when God…was pleased to reveal his Son in me so that I might preach him among the Gentiles, I did not consult any man, nor did I go up to Jerusalem to see those who were apostles before I was…
Apparently, these false teachers were saying that Paul does not speak for the other apostles, some of whom were still in the city of Jerusalem.
Perhaps they made the argument that the other apostles felt as they did, that the Gentile Christians should be circumcised and keep the law. And therefore, Paul was wrong not to require they keep the custom of the Law of Moses.
Paul, therefore, is forced to present his credentials as someone called by Jesus. And that his message to them was only what Jesus Himself had revealed to him.
While the apostles in Jerusalem are primarily seeking to teach Jews, Jesus has given Paul the special mission and revelation to the Gentiles.