How is the pride theme essential in "A & P," "The Scarlet Ibis," and "A Clean, Well-Lighted Place"?

Each of these three short stories deals with the thematic idea of pride in some respect. To answer your question, it is important to understand what you mean by essential. For my answer, I will work under the assumption that this means it is necessary to understanding the meaning of the text as a whole. I will discuss each story separately.
In John Updike’s "A & P," Sammy believes that he is coming to the rescue of the young attractive girls who enter the grocery store in which he works. His boss criticized the girls for wearing swimsuits in public, saying they need to cover their shoulders. In a proud gesture of heroism, Sammy rips off his apron, making a statement in the girls’ defense. Ironically, though, the girls do not notice his gesture, having left the premises without saying a word. In this story, Sammy is proud of himself for behaving so chivalrously, despite having ogled the girls as they shopped. The failure of the girls to notice him suggests that his masculine pride was misplaced and insignificant.
In "The Scarlet Ibis," Doodle’s older brother constantly tries to get his developmentally disabled and ill sibling to perform tasks of which he is clearly unable to complete. The narrator admits that he was partially motivated to force Doodle into performing these tasks because he was angry at having a brother who was different. Thus, the narrator’s pride is the source of his resentment toward Doodle. When Doodle dies during the storm, it is partially because the narrator abandons him. Because Doodle did not live up to his brother’s expectations, the narrator left Doodle to die alone. If the narrator hadn’t felt shame over Doodle’s abilities, he never would have forced Doodle to push himself so hard.
In Hemingway’s "A Clean, Well-Lighted Place," the two waiters in the cafe have different views on the elderly man who stays so late at night. The older waiter comes to the man’s defense because he has a similar need as the old man. The older waiter leaves his shift and wanders until he finds the titular “place” so that he doesn’t have to be alone while struggling to sleep at night. This story, I think, is least connected to the thematic idea of pride, but one could argue that the younger waiter, who selfishly wishes the old patron would just leave so he can go home, is motivated by a kind of selfish pride, believing that his needs are more important than that of the old man. The older waiter and the old man are similar in that they have abandoned their pride because of their understanding that life is utterly meaningless. Pride, then, is a tool of the individual to ascribe meaning in a world that lacks any.