When Paul's enemies found out that Paul was still alive, reinforcements came down from Jerusalem.  It was all out war.  They followed him down to Antioch of Syria, (Acts 14:24-15:2) but could not make another open attempt on Paul's life since Paul had many friends nearby.  So they developed an alternative strategy.  The enemies of grace would invite Paul to debate, and would dictate the  ground of the debate.  That ground was carefully selected to gain strategic advantage in the battle for the hearts and minds of the onlookers.  And that strategic ground was circumcision.

The debate over circumcision advanced a powerful three pronged attack against the doctrine of grace:  Scripture, Tradition and Logic.

SCRIPTURE:  God gave the commandment for circumcision in Genesis 17:9-14 to the patriarch Abraham.  It was not simply opinion, it was the Abrahamic covenant set forth in the Word of God.  So important was this covenant that hundreds of years later, when Moses postponed circumcising his own son, God very nearly cut Moses' life short for this act of disobedience.  (Exodus 4:18-31)  Because every male Jew at the time had been circumcised, Every living Jew knew the importance of circumcision.  The enemies of grace therefore felt they could undermine the doctrine of grace by appealing to a law with which everyone was familiar.

TRADITION:  In Acts 15:1, circumcision is regarded by many of Paul's Jewish contemporaries as having soteriological (saving) significance.  That this was not a passing fad, but a deeply entrenched tradition, can be demonstrated by the fact that similar statements were still being advanced in Rabbinic literature at least 300 years later.

"Circumcised men do not descend into Gehenna and At the last Abraham will sit at the entrance to Gehenna and will not let any circumcised man of Israel go down there."

Rabbi Levi, Circa A.D. 300

"Circumcision will deliver Israel from Gehenna and Only in certain cases is the saving power of circumcision believed to be ineffective."

C.E.B. Cranfield's Commentary on Romans [1]

Because these sentiments run from the Jerusalem Counsel to at least the mid-fourth century, they provide insight into the strength of this tradition.  If the opponents of grace hoped to win their case, they clearly could not have chosen an issue that held more emotional sway with the average Jew.