There are several social issues at work in "A&P" that one could write about in a literary essay of argument.
A prominent issue that Updike weaves into the story is varying perspectives on social conformity. The three girls that come into the store wearing only bathing suits, and Sammy, the cashier, represents a teenage generation that feel a need to push back against the social norm of what is appropriate attire in public. Lengel, the store manager who tells the girls that they must be "decent" when they come into the store, represents the older generation that wants to uphold a more conservative view of what decent attire means.
A feminist reading of the story could argue that the girls are attempting to claim their sexuality in an act of nascent feminism, but they are shut down by the older male establishment and society that is not ready to support them.
Through Sammy's observations about what the girls purchase and his own parents' buying habits, he brings to light the social divide between the working class and upper middle class. His failure to catch the notice and admiration of the girls makes his sacrifice all the more poignant at the end of the story. Sammy has, after all, dubbed one of the girls "Queenie" and realizes that she is out of his league.
A fourth social issue that could be analyzed in an essay is the rise of consumer culture and mindless consumption even at the grocery store. This comes to light in the descriptions of the things that Sammy observes the customers buying.
And finally, the objectification of the girls evidenced by the lascivious gaze of the butcher and the comments that pass between Sammy and Stokesie could make its way into an argument about the dehumanizing of the girls even by their would-be defender.