"A Conversation with My Father" is a story-within-a-story. The one story, of course, is about the relationship of the daughter and her dying father; the other is a story composed by the daughter which the father critiques.
Initially, the father asks his daughter to write a story for him, one that describes life without sympathy and with recognizable characters in the manner of Maupassant and Chekhov. So, the daughter writes a bare-bones story that is, as she describes it, "an unadorned and miserable tale." But, the father is displeased, feeling that his daughter has left out too much detail because he was a physician and then an artist who has always been interested in craft and technique. So, she writes another story that includes much more detail, but since she feels that "everyone real or invented deserves the open destiny of life," she ends the story in a manner that is again dissatisfying to her father, although he agrees that the mother meets her end. "You were right to put that down. The end."
In response, the daughter tells her father that "it is not necessarily the end, Pa. It doesn't have to be." Because of his being on oxygen and clinging to life with a debilitated heart, the father contradicts her, contending that all life is a tragedy. Still young, his daughter disagrees, telling him that the mother in her story can yet find a job and move on with her life. Irate, the father declares, "Tragedy! You, too, will you look it in the face?"
The underlying message here, then, is that the father struggles to make his daughter accept his imminent death.