Itto's knowledge and understanding of various philosophies has helped him understand people to such a degree that he's able to gain their respect, so to say. So in this instance where his child is being held hostage, he was able to talk them into letting Diagoro go because there was nothing to gain from it. After his son is no longer in danger, Itto does what he knows best. Kills everyone who tries to bring him and his son harm. What a boss.
