Sammy, the protagonist of A & P by John Updike, would like to imagine himself as a chivalrous hero, protecting young ladies from evil and thereby coming to their notice. He thinks of his grand gesture at the end of the story as an admirable effort to be true to principles and stand up against the shibboleths of small-town society. From a feminist, or generally an adult, perspective, though, it more resembles the act of a sulky teenager.
The first piece of evidence for Sammy's complicity with patriarchy is that he exemplifies the male gaze; both the protagonist and the story itself view the young women mainly through the perspective of male sexuality, with Sammy in particular obsessed by the bodies of the girls. We also see here an alliance between patriarchy and class privilege, with Sammy's sexual attraction to the wealthy young women, who at first seem spoiled, entitled, and inconsiderate, causing him to be complicit with them as they flout the social norms of his town.
The next type of evidence we see for sexism is the way Sammy ranges from dismissive to hostile in his thoughts about women who do not appeal to his sexual fantasies, thinking of them as "houseslaves in pin curlers." We are introduced to this at the beginning of the story when Sammy thinks of the middle-aged woman he is checking out as follows:
She's one of these cash-register-watchers, a witch about fifty with rouge on her cheekbones and no eyebrows ...
If we think outside Sammy's self-involved patriarchal universe, a customer has every right to insist that a cashier ring up her groceries correctly rather than making mistakes because he is ogling girls in bathing suits rather than focusing on his job. Sammy's sexism surfaces in the way that even if women are the customers who (albeit indirectly) pay his salary, he regards them with annoyance or contempt if they are not sexually appealing.