The narrator's father believes that the jokes belittle the people she is writing about and also belittle the type of story-telling he is challenging her to write.
When he hears the first version of the story, the father's response is to reference accomplished Russian writers. He mentions Chekov and Turgenev and implies that they would have written a story that were more serious and sensible.
The humor in his daughter's story does not fit his sense of what he has asked her to write.
He asks his daughter to write a "simple story" about "recognizable people"...
The father is not against humor, per se, but wants his daughter to write a particular kind of story that deals directly and simply with the facts of life. He says at one point, "I do not object to the facts but to people sitting in trees talking senselessly..."
At the story's end, he questions when his daughter will face reality, which for him includes the fact of tragedy (and possibly of failure as he regards his daughter).
This insistence on tragedy as a fact does not match with the narrator's view of life, nor her view of fiction. She sees the possibility for a happy ending in her story (and, by implication, for herself). There is a chance that things will change, importantly, for the better. The present is therefore not an absolute indication of the future.
Humor, and its play on multiple meanings, is entirely appropriate for stories written by someone with her worldview.
The narrator believes that in both literature and life, a plot that follows "the absolute line between two points ... takes all hope away."
Her father sees the present as a definite indicator of the future, which makes the present, in some cases, a condemnation and a tragedy. For him, there is no place for humor in a story dealing with this perspective as a description of reality.