It was the Saturday of the big game versus Saxon Hall. It was the last game of the year so everyone was at the game, except for Holden who was on watching from the top of the hill.
Holden tried to punch Stradlater while he was brushing his teeth so it would "split his neck" but missed and barely grazed his head. Stradlater punched him and gave him a bloody nose but felt bad so he told Holden to clean himself up while Holden was still yelling at him.
Holden got tired of waiting to go back home after he was kicked out of Pencey Prep so he decided to leave three days early. This was a form of alienation and rebellion of society.