All the logic in the world will not help you, or them, understand these emotions. Emotions are not logical. Department heads might begin mindlessly protecting territory, losing sight of organizational goals, sabotaging needed changes, even destroying a carefully designed quality initiative before it gets off the ground. No, but they are. You will fare much better by understanding what they do see before you begin swaying them toward your viewpoint.
People are people.
They can get territorial about anything they perceive as valuable. Your efforts to implement quality changes will create territorial games. They shouldn't, but they will. Territorial feelings are easy to anticipate. Figure out who might feel as though the initiative is invading their territory.