In part 1 of this sad account of a man's "indoctrination" on how a black man is supposed to live under Jim Crow laws, Richard is, indeed, between a rock and a hard place. Morrie is adamant that Richard had done the unthinkable by speaking to his white patron only using his name, without addressing him as "Mr."
Either way would have been a bad thing for Richard. All he could do was to tell Mr. Pease that he does not remember calling him "Pease". However, that if he did do that, that he feels very sorry.
Pease takes it as an admission and
he spat, slapping me till I bent sideways over a bench. Morrie was on top of me, demanding...
There, Morrie shouts
Didn't yuh call 'im Pease? If yuh say yuh didn't, I'll rip yo' gut string loose with this f-***' bar, ...Yuh can't call a white man a lie 'n' git erway with it...
At this point Richard realizes that all that they want is for him to leave the job. He realizes this as he sees the two men ganging up on him. He basically told them (to avoid any more abuse) that he will just leave. They gave him a minute to leave. Upon telling his folks, Richard says that they called him a fool for not keeping "his place" and for annoying a white man, particularly, his boss.