We know that "In the American Society" is written from a first person point of view because of the pronouns used in the story. The narrator presents the conflict through her own perspective, using pronouns like I, my, our, and we as she relates the events. Check out this segment of the text with those first person pronouns identified:
She also invited Mona and me to the going on, as "demi-guests" to keep Annie out of the champagne. I wasn't too keen on the idea, but before I could say anything, she had already thanked us for generously agreeing to honor her.
Of course, anything inside the quotation marks of dialogue won't count as you're looking for these first-person pronouns, so be sure to focus on narrative sections of the text.
First person point of view helps intensify the conflict in this story. Because the narrator's mother wants to join a country club, the entire family is fairly dragged to a "bon voyage bash" for Jeremy, a friend of one of the members. At the party, the narrator watches as Jeremy insults her father; as a young woman, she is essentially powerless to intervene on his behalf in this context. She presents the conflict, initiated by Jeremy, through the conversation that transpires when Jeremy loudly insults her father and then tries to force him to take off his shirt in front of everyone.
After the family leaves, the strength of the family is particularly clear because of the first-person narration of this young girl. Though they have all witnessed her father being insulted, the family is proud of his act of defiance and follow the leadership he provides.