How will a closer analysis of the author's claim and the structure of the writing help you to learn more about the reading?
In your question, I take it that by "the author's claim" you mean Sedaris's basic thesis of the marginalization of gay people or of anyone who is different or has some quality of Otherness. The structure of his writing is basically one in which the narrative is geared toward finding humor in this phenomenon. But in Sedaris's treatment, it's humor with a very sharp edge. And anyone who has been bullied or pushed down for any reason can identify with his account of how he is treated.
What strikes one about his narrative structure, moreover, is the effectiveness of his placing people's reactions to him in a broader cultural context. Speech class, for instance, was one of numerous control methods in the 1960s by which kids who departed even slightly from a behavioral norm were made to feel substandard. Though Sedaris's interpretation of it rings true as something directed against boys suspected of being gay, it had this broader purpose, like other mechanisms in the school environment of that time. (And girls were sent to speech class as well, contrary to his assertion.) Though it is hard to believe, one can't, in looking back on that time, dismiss the fact that there were educators who deliberately wished to humiliate kids for various reasons. The claims made by Sedaris about environmental factors in the school and the home are both valid on their own terms but are indicative of more general efforts in a conformist culture. In other words, gay people were (and still are) focused upon in an exaggerated form of what goes on anyway in relationships governed by the seemingly omnipotent authority figures, including the all-knowing parents. This dual factor of abuse directed against specific Otherness and against more general nonconformity is a subtext of Sedaris's narrative structure and makes his message all the more powerful.
The effort by Sedaris's father to make him learn the guitar is both hilarious and horrifying. Sedaris's deliberate political incorrectness in his description of the guitar teacher, Mister Mancini ("Mister" is often spelled out), who is a little person, is especially significant. One would think Sedaris would feel some sort of bonding with the teacher, who is stared at and talked about by people at the mall when he's doing nothing more obtrusive than ordering a hamburger. Sedaris's revealing his actual preference for being a singer backfires, with Mancini telling him coldly that he "doesn't go in for that scene" when all the boy has done is sing the tune from a TV commercial. It is a revealing moment, to say the least.