Cinis invaded Mt. Hirota long ago during the war that created the great cataclysm. When Cinis invaded, Kaz was just a baby. His parents hid him away from the army that Cinis ruled over, so they couldn't find him. Cinis' army killed every last samurai brother and sister besides Kaz, including his parents. Cinis should make a call back to this during the final fight, explaining how he had his men ravage Kaz's mother over and over while his dad was pinned down.
This backstory should serve as a very emotional motivation for Kaz to help the players.