Why is Lieutenant Kotler reluctant to talk about his father? How does this arouse the Commandant’s suspicions?

Lieutenant Kotler's father had "disagreements" with the German government. Although Lieutenant Kotler pretends to know little of this, it becomes obvious that he is overcompensating for his father's indiscretions. The Commandant suggests to Kolter that,

“One hears tales of this from time to time. Curious fellows, I imagine. Traitors, others. Cowards, too. Of course, you have informed your superiors of your father’s views, Lieutenant Kotler?”