Why does Harold Krebs in Ernest Hemingway's short story "Soldier's Home" seem to live his life after the war as an existentialist?
Your question is interesting because it gets to the heart of a phenomenon we witness in returning veterans from almost every war: the inability of many veterans to remain connected to their society. Your question defines this behavior as existentialism--the importance of being over experience--in which the person no longer believes that any particular action is worth taking because there is no longer any meaning in taking action and engaging with the broader society.
This phenomenon is now more widely attributed to what we call Post Traumatic Stress Disorder, a veteran's reaction to coming home to civilian life after having experienced constant danger, anxiety, stress from the threat of either dying or being wounded--home to a society that fails to understand what the veteran has been through. Hemingway's "Soldier's Home" describes a text-book case of this problem.
Krebs began his life in the army as a completely conventional volunteer from small-town America:
Krebs went to the war from a Methodist college in Kansas. There is a picture which shows him among his fraternity brothers, all of them wearing exactly the same height and style.
Here, Hemingway establishes that the protagonist of this story is a typical American college student, no different from his classmates (they all wear the same kind of clothes), and we expect, therefore, that he will have the same reaction to the experience of war that most of the others have.
Another important detail early in the story is that Krebs returns from the war long after all the other men in his town and "people seemed to think it was rather ridiculous to be getting back so late, years after the war was over." Because of his late return, Krebs misses the communal experience of the town celebrating the veterans' return, and by the time he returns, the townspeople and other veterans have moved on and no longer think much about the war. We also learn that Krebs wants to talk about what happened to him, but no one is interested in listening--this is the beginning of Krebs' alienation from the rest of society.
Krebs' existential behavior--his lack of engagement with the larger society--is summed up in a phrase that Hemingway uses several times when he describes Krebs: "It wasn't worth it." Whether Krebs is considering a relationship with a girl in the town or getting a job, his response is always that it's too complicated and not worth the effort. In this context, it's also worth noting that Krebs' war experience included several of the most horrific battles in which Americans participated, a detail that Hemingway adds in order for us to understand the underlying cause of Krebs' mental isolation.
Even though, at the end of the story, Krebs understands that he finally must engage with the world--like getting a job and engaging with the world again--he exhibits no enthusiasm for this decision because, as he notes, his uncomplicated life "is all over."