"...to whom we did not yield submission even for an hour, that the truth of the gospel might continue with you."
The apostle Paul met with Peter, James, and John because of some sort of provocation by false brethren, who had smuggled themselves into the church in order to lure the church back into spiritual slavery. But those three apostles knew the Gospel, too, and heartily endorsed Paul -- and probably shut up the trouble-makers for good (if this was a modern church, then the trouble-makers would have gone off, started another church, and called themselves "restorationists").
Because of the insight given to him by the Gospel, Paul correctly identified those false brethren as enemies of God. As a result, Paul and the other apostles did not conceded anything to them. No doubt they reasoned with them, exhorted them, and pleaded with them to see the condemning error of their legalism. But when it came to the bottom line, the apostles did not concede an inch of doctrinal ground.
Why were they so tough? Because they accurately saw themselves as guardians of the Gospel, and they were looking beyond the conflicts of today to the redemption of tomorrow. It was their job to defend and preserve the Gospel. Future generations yet unborn were depending on their toughness. They didn't compromise. They didn't negotiate a half-way point with the works-righteousness trouble-makers.
How unlike so many modern American Christians, who will trade away their eternal birthright, and the eternal birthright of their children, in exchange for a little bit of temporary peace. All the old denominations -- the Presbyterian Church USA, the United Methodists, the UCC, the Episcopal Church -- are ruined today because, long ago, weak men compromised with liberalism instead of driving it out. They did it in the name of "peace and unity."
The Gospel is more important than everybody getting along. Churches often split over ridiculous things, and often church-fights are nothing more than a carnal clique demanding its own way. But sometimes there are fights worth fighting. Preserving the integrity of the Gospel is one of those fights worth fighting.