What social statement does Sammy think he is making by quitting his job in A & P?
I think the social statement that Sammy is trying to make is a statement against his manager's determination and support of what society deems "decent" clothing inside the store. By quitting, Sammy believes that he will be Queenie's knight in shining armor and hero:
The girls, and who'd blame them, are in a hurry to get out, so I say "I quit" to Lengel quick enough for them to hear, hoping they'll stop and watch me, their unsuspected hero.
Sammy is upset with Lengel's treatment of the girls. It begins when Lengel sees the girls and immediately tells them that his store "isn't the beach." He does not explain it any further at first, and Lengel expects the girls to immediately know what he is talking about. Queenie tries to defend herself and her friends by saying that they only came in to buy one item, which gives Lengel the opportunity to tell the girls what is "decent":
"We want you decently dressed when you come in here."
Queenie is visibly upset at the remark, and she defends herself and her friends by saying that they are decent. Lengel's response is to bring up and enforce store policy. He tells the girls that they must have their shoulders covered up in order to be in the store:
"Girls, I don't want to argue with you. After this come in here with your shoulders covered. It's our policy."
Sammy rings up their purchase, the girls quickly begin leaving, and Sammy quits. He is hoping to appear heroic to the girls by fighting against the store policy. It is a weak attempt to be a "bad boy":
Policy is what the kingpins want. What the others want is juvenile delinquency.
The social statement is not Sammy's only reason for trying to come to the rescue. Right after he quits, Sammy tells Lengel that he "didn't have to embarrass them," which shows that Sammy was very much empathizing with the girls' situation. He is quitting to show the girls that he understands their situation and feelings. He is hoping that his efforts will warrant the attention of Queenie. Unfortunately the girls do not notice his actions, and they are long gone by the time Sammy exits the store.
Sammy quits his job to protest his boss’s treatment of the girl he likes.
In the story, Sammy is trying to find himself. He is self-conscious and socially frustrated. When he sees the girl being treating in a way he thinks is unfair, he tries to be her hero. His reaction to the “policy” that shoulders must be covers shows his issues with society.
That's policy for you. Policy is what the kingpins want. What the others want is juvenile delinquency.
Sammy is not sure what to do. He has no power, but he wants to take a stand. He feels that the girl has been wronged. He wants to make it right. Since he is powerless to do so, he takes the only power he has and quits.
The futility of the gesture is a lesson in life. Part of growing up is realizing when to pick your battles. There was nothing wrong with pointing out that a bathing suit is inappropriate attire in a store. In his sexuality-driven sentiment, Sammy could not see that. He took a stand, but he was the only one affected.