The historical record that Paul references in this testimony is apparently a period of tension and outside pressure on the Church in Antioch, where Paul and Barnabas were based as teachers and evangelists. Representatives from the Jerusalem Church had come to evaluate the outreach at Antioch, and were disturbed by the Christian liberty being exercised by Gentile converts to the faith. Paul perceived these men to be an enemy force, "spying out" the Antiochan fellowship in order to bring a negative report back to Jerusalem. He realized if the Judaizers got their way, strict adherence to the Mosaic law would be forced upon the Gentiles in the Church, and that would stifle the evangelistic effort.
If Paul seems to recount the events without charity for his Judaizer rivals, it may be helpful to remember the context in which he is writing his epistle to the Galatians. After the initial confrontation in Antioch, the differing parties brought their cases to a council of apostles and elders in Jerusalem. There Paul's viewpoint finally won the day, and it was decided that the Gentiles would only have to endure a few rules: eat no food that had been offered to idols; eat no blood; eat no animal that had been strangled; and avoid sexual immorality [Acts 15:29]. But years later, the Judaizers were again proselytizing Gentile converts, this time in the region of Galatia. The apostle had believed this matter was settled, and was extremely disturbed that an old wound was being aggravated.
Too much can be made of Paul's language in describing the council participants: how his words could be read as a diminishment of their authority over him. He is not here attempting to belittle the leaders of the Church at Jerusalem, but to assert that when he and Barnabas met with those who seemed to be "the pillars of the faith," the two little missionaries persuaded them with their testimonies of what God had wrought among the Gentiles. Principally, Paul mentions this to emphasize to the Galatians that titles and reputations are not a substitute for sound doctrine. The Judaizers coming to them may have had fine pedigrees and important positions, but they only offered a discredited set of teachings. Paul insisted that the Church hold onto the doctrine of grace instead of embracing a salvation of works, be it through circumcision or the keeping of any other Mosaic law.
In the end, Paul had fought aggressively against the intrusion of the Judaizers at Antioch, and he was willing to contend with them again as they pestered the Galatian Church. He could testify that he never "gave place" to them--"no, not for an hour"--because he knew the importance of standing firm for grace. We have this model in scripture so that we will be just as aggressive contending for the faith. If we don't confront false teaching, we leave new saints vulnerable to its error. The apostle John warned us not to even be hospitable to a false teacher, so as not to be a partaker of his work [2 John 10]. If we are not confronting the spread of false doctrine, we will share in the blame for the weak-minded brethren that are led astray. It is not only our duty to grasp hold of the truth ourselves, but to defend it against the attack of Satan for the sake of other believers.
Essential Thought: Our love and concern for the Church should motivate us to challenge falsehood wherever we find it.