The official charge is probably blasphemy. It is couched in the terms that Abinadi was so careful to propose, that God himself should come down among the children of men. Noah and the priests must deny this, or they would have to admit they had been teaching false doctrine.
Noah gives Abinadi the chance to recant. Why would he do this? The most logical reason is that he would understand the possibility of Abinadi becoming a martyr, and therefore becoming a rallying point for religious opposition to Noah. If Noah could have Abinadi recant, then the potential damage would be eliminated.