Luther did not go to rome when he was summoned by the pope because

It was likely he could face death on charges of heresy.

A hundred years before Luther began his reformation efforts, Czech reformer Jan Hus was put to death by the Roman Catholic Church for being a heretic.  There was much fear Luther would be treated like Hus had been treated.  Luther had the advantage of having a strong prince in his territory in Saxony who was intent on protecting Luther as one of his subjects, preventing the pope (seen as another ruling prince) from interfering with the sovereignty that Elector Frederick the Wise of Saxony asserted over his domain.