Here's a breakdown of why:
* Centaur Tradition: Centaurs, as a species, value secrecy and generally keep to themselves. They believe in maintaining a distance from the wizarding world and consider it unwise to interfere in human affairs.
* Firenze's Actions: Firenze, despite the centaur tradition, chose to help Harry and his friends. He even intervened in a fight with the other centaurs, which was seen as a violation of their internal rules.
* Bane's Perspective: Bane, being a strict follower of centaur tradition, saw Firenze's actions as a betrayal. He believed Firenze had jeopardized the centaurs' safety and standing by involving them in the wizarding world.
* Consequences: Bane and other centaurs who held similar views exiled Firenze from the herd. This was a punishment for his actions, meant to maintain order and their own sense of security.
While Firenze's decision was ultimately beneficial to Harry, it was a significant breach of centaur tradition and a deeply personal betrayal for Bane, leading to a lasting rift between the two.