Fitz says that Deklan started the fight in retaliation to criticism and subsequently killed the teacher. Deklan quickly defends himself from this by claiming that the real reason the teacher died was because Fitz tried to intervene in the fight and accidentally hit the teacher with a kettle when he meant to hit Deklan.

In that moment, Deklan goes along with the story that he, himself, was the one to start the fight.

But Mogau realises the logical inconsistency in Deklan’s story because… in the moment of his initial statement, Deklan’s story is that Fitz was the one to start the fight and eventually kill the teacher.

These two statements can’t be true at the same time… so Deklan boiled himself into a hole and revealed himself to be lying. And so… we know that Deklan is the murderer!