In the context of Dune, it is a question of whether you can maintain your logic in the face of pain or danger, or whether you will be ruled by your instincts when push comes to shove. And that question is a vitally important one when taken in the context of choosing a new leader or ensuring that someone (in this case Paul Atriedes) is able to handle the pressures of their given task. An animal will be ruled by its instincts while a human can overcome them by force of will. If you are not a human then you are an animal. Animals can still be treated with respect, but they are unfit for leadership roles because a frightened animal driven by fight-or-flight response is unpredictable and dangerous. A cornered king can be reasoned with, but a cornered animal will gnaw its own leg off to escape a trap.