Why was Nat bothered that they were killing the bear?

Nat was bothered by the fact that the bear was blind.... purposely blinded and attacked for entertainment.

The crowd roared. Even over the din you could hear the bear bellow with pain and rage. His face was turned full in our direction as he tossed up his head, blood dripping from his neck, and in sick horror I realized that he could not see.

Harry's cheerful open face was alight with excitement. "Of course—Blind Edward—they put out his eyes, for better sport." He shouted in sudden glee. "Look there!"