Bite me or love me
An order from the general was absolute and a strict punishment awaited those who disobeyed them. Although there weren't many rules when it came to what happened between the students themselves, the same couldn't be said for those who were above them.
If you broke the rules enough times, then you would be led to an underground dungeon. The school couldn't just kick you out. Those who went in almost never came back out, and the ones who did come back, came as different people.
There was also a rumour that had been going around that the students who were sent into the dungeon came back without any abilities at all.
Because of this, even Vorden was worried about going up against a general of the school. Perhaps he could use his family's power to influence the military's decision about Duke, but that would require evidence and a lot more than a single testimony from Peter.
So the group had no choice but to follow Duke's command.