I would want to focus on the presentation of the central character, Krebs, and how he is presented as an anti-hero, or a central figure that displays the opposite of many of the traditional characteristics of a hero figure. Krebs is above all apathetic, detached and resists involvement or commitment of any kind in life. His character is a demonstration of the impact of war on young men who came back utterly changed. Exploring his character and how it is presented should give you ample scope for an essay.
This story has an ambiguous title, interestingly. Does Soldier's mean the soldier is or does it mean his home or does it mean a retirement home? It does not mean the third, but the story waivers between the other two. You could write about this ambiguity; that is, how the soldier is home, but the house is not truly his home and he must go somewhere else.
Although the soldier is home, he cannot stay since he has to act childish around his mother; Kerbs even reverts to calling his mother "mummy." Sick of the lies that he has felt forced to tell his mother, Kerbs knows that he must leave in order to live. Like so many of Hemingway's characters, especially Nick Adams, Kerbs must leave the world of hypocrisy and establish order in his world. For, doubt and apprehension cut off physical action, certainly action of the will.One must establish a pattern (see pars. 9 and 14) One must be stoic, holding on against odds. Hemingway's male often makes a style out of despair, and Krebs tries to do this.
Researching Hemingway's themes will be a great help to you. One axiom of Hemingway's is Find rules to live by. yet, if you don't expose yourself, you won't really live.