The Jerusalem Council
Gal 2:1,2 Fourteen years later I went up again to Jerusalem, this time with Barnabas. I took Titus along also. I went in response to a revelation and set before them the gospel that I preach among the Gentiles. But I did this privately to those who seemed to be leaders, for fear that I was running or had run my race in vain.
The event Paul refers to in this and following verses is found in Acts 15. That is " Some men came down from Judea to Antioch and were teaching the brothers: 'Unless you are circumcised, according to the custom taught by Moses, you cannot be saved.' This brought Paul and Barnabas into sharp dispute and debate with them. So Paul and Barnabas were appointed, along with some other believers, to go up to Jerusalem to see the apostles and elders about this question." Acts 15:1,2
But what does Paul mean when he says he just intended to meet with the leadership, “for fear that I was running or had run my race in vain.”? For we note Paul was quite confident of his convictions. And as we noted from chapter 1, Paul didn't feel he needed the other apostles to validate his gospel. For if that had been the case, he would have gone to them years ago prior to his preaching of the gospel. Rather he was concerned as to whether or not these kinds of false teachers were among the reputable leadership of the church at Jerusalem. And if so, he was concerned about their power. And indeed he had cause for concern, for in that case it would mean that Peter, John and James, who were the heads of the Jerusalem church, had failed to deal with them. And why? Likely because Peter, John and James were afraid of the popularity of those guys. (Very common, even among the apostles, to fear issues which threaten one's popularity) In fact Paul gives an instance of this in the case of Peter later in this chapter.
Thus if Paul was going to Peter, James and John to deal with the false teachers within their own church, he was going to have to get them together in private, where their flesh would be more free from the pressures and power of popularity inherent in public meetings. Now the issue would be as to whether the false teachers had power in the private meeting - which leads to the next verse.