With climax being the point in a plot that creates the greates intensity, suspense, or interest, this point in John Updike's "A&P" is the action during which the conflict is resolved, or an attempt is made to resolve it. For, in actuality, Sammy's rebellious action meant to impress the girls does not resolve anything.
When Sammy tells Mr. Lengel that he quits, the employer essays to avert disaster for Sammy, "I don't think you know what you're saying." However, in his ego-centered rebellion, Sammy states that he believes that
once you begin a gesture it's fatal not to go through with it"
and he walks out, anyway. Once outside, he notices that the girls, for whom he acted so chivalorously, have departed. Moreover, Sammy notices that Lengel is in his place with his back stiff and Sammy's stomach
kind of fell as I felt how hard the world was going to be to me hereafter.
While Sammy may have realized that the complex world of adult requires compromise, he is left in limbo between the two worlds himself, with no resolution to the conflict that he has sought to end.
The climax of the story is when the protagonist gets quite upset at his A&P manager for his treatment of Queenie and the rest of the bathing suit girls and quits his job in front of everyone.
This event is simple to explain: He is a teenager, he is smitten, and he wants to make an impression on the girls without thinking about the consequences. Plus, he is quite fed up already with his job, his manager, and everything around him. He is not happy anyways, but the girls may have been the excuse all teenagers need to explain impulsive behaviors.
Nothing was gained. Even the protagonist admits it. Yet, there is so much ego and risk involved that, for a teenager, this wouls have been a nightmare to explain. However, he (as a young man) did what he thought was best (albeit, idiotically) but he could still say he has a story to tell when he gets older.