Why did Paul refuse to give in to the Jewish leaders' demand that the Gentiles be placed under the Mosaic law?

Les teaches that the issue at Jerusalem was whether the truth of Paul’s gospel would continue. If the Jewish leaders had convinced Paul that Gentile believers had to subject themselves to the Mosaic system, Christianity would have died; it would have been the end. Paul did not give in, thanks to the sovereign God of all grace. This was where everything hung in the balance: had Paul given in, the gospel as we now know it would have died, but God would not allow that. Later, James, Cephas (Peter), and John, who seemed to be pillars, perceived the grace given to Paul and gave him and Barnabas the right hands of fellowship, agreeing that Paul should go to the heathen/Gentiles while they went to the Jew.