It is interesting that Hemingway chooses the father, rather than the mother as the observer of his child; also, it is rather curious--if not unnatural--that the mother does not become involved in the situation involved in the short story "A Day's Wait."
Be that as it may, the father's initial close observation of the boy's condition seems incongruous to his lack of anxiety about his son's illness when he says, "I'll see you when I'm dressed." Here the reader may well wonder if Schatz has had the flu before. Then, when the doctor is called and he explains to the father (still no mother in the scene!) that "there was no danger if you avoided pneumonia," the narrative seems more realistic.
Nevertheless, the father fails to sense the magnitude of his illness for the boy when he tells him,"...you don't have to stay if it's going to bother you." For, the father simply feels that the boy is worried about his contracting the flu germs. Instead, however, the boy speaks of what he believes is his approaching death.
Because of the father's lack of intuition and perception, Schatz faces alone the greatest of existential crises: the possibility of death. Schatz bravely "holds" himself against nothingness in a conflict marked by his sense of terrible aloneness. And, when the father finally comprehends the struggle of his boy, he speaks to him as though he is merely a fellow soldier, "Poor old Schatz....." only consoling him logically. Perhaps, Hemingway wishes to convey that this struggle with nothingness is, ultimately, one that man must endure alone.
Finally, it is a detached narrator/father who observes that his son's "gaze" at death relaxes, but he "cried very easily at little things that were of no importance." This emotional response of Schatz to little things indicates the trauma that the boy has suffered, his release of his courageous attitude, yet the father offers no physical or emotional comfort to his son. This lack of reaction on the part of the father suggests the point of view that each person must face alone existential issues.