The answer to this question can be found in Chapter 12. The essential reason is that the young warriors came to believe that Red Cloud was not sufficiently opposed to the white people.
In this chapter, the Sioux are extremely angry because of white incursions into the Black Hills of South Dakota. This area was sacred to the Sioux. The younger warriors of the Sioux were eager for war. They eventually rejected Red Cloud as leader in favor of Crazy Horse and Sitting Bull. Crazy Horse and Sitting Bull had never lived on a reservation. Because of this, the younger men trusted them to resist the whites more vigorously than Red Cloud would.