Given the fact that O'Connor's "My Oedipus Complex" depicts one of the Psycho-Sexual Stages of Development, the Phallic stage, one can see where the title and the story emerge from.
Larry, the only child of his parents (initially), receives complete and undivided attention from his mother given his father is away fighting in WWI.
Upon his father's return, Larry no longer obtains his mother's undivided attention. Instead, she devotes all of her energy to his father. Larry becomes very jealous (notated by Freud's Oedipus Complex) and wishes to take his father's place in the relationship with his mother.
Later, the arrival of a new child, Sonny, places Larry's father in the same shoes Larry was placed in when he returned from the war.
There could be many different thesis statements which would define the relevancy of both the text and the use of Freud's theology.
1. Both Larry and his father possess characteristics typical to one deemed "stuck" in Freud's Phallic Stage. (How are they characteristically stuck in the Phallic Stage? Examination of both Freud and the text.)
2. Larry's mother is responsible for his inability to accept his father's place in their lives. (Paper will examine Larry's mother.)