What lesson does Buck learn about the law of clubs and fang?

Buck learns that the law of clubs and fang signifies the harsh and brutal nature of survival in the wild. This lesson comes from his experiences as he adapts to a new environment where strength, aggression, and the willingness to fight or submit are vital for survival. The "club" represents the violence that humans can wield to assert control, while "fang" represents the instinctual behaviors of dogs and wolves that are necessary for survival in a brutal landscape.

Through his journey, Buck witnesses the consequences of failing to comply with these harsh laws, understanding that in the wild, power dynamics are dictated by strength and the capacity to inflict harm. This realization forces him to transform from a domesticated pet into a more primal version of himself, showcasing the brutal reality that governs life in the wilderness, where compassion is a weakness and survival often comes down to dominance.