Since his experience in the war, Krebs no longer feels at home in the small Oklahoma town where he was raised. The people in the town want to basically carry on as before and forget the war, but because of his horrible experience Krebs can no longer relate, not to his parents or to the girls he sees on the street. I think Hemingway meant the title ironically. Krebs no longer has a home. It was one of the reasons why Hemingway himself and several of the characters in his literature expatriated to Europe in the 1920s.
Several of Ernest Hemingway's stories deal with soldiers coming home from World War I. The war was the most devastating the world had ever seen. It caused millions of casualties, dead, wounded, and also those suffering from, what we now call, post traumatic stress disorder. Both Jake Barnes, from the novel The Sun Also Rises, and Nick Adams, a character in many of Hemingway's short stories, have, in some way, been debilitated by the war both physically and mentally.
Harold Krebs, the main character in "Soldier's Home," is suffering from PTSD. He has obviously seen horrible things in the war and, at first, doesn't wish to speak about them. Later, when he wants to talk, nobody wants to hear about the "atrocities" of the war. Rather, he says, he makes up lies. We assume these lies involve heroic acts. Krebs feels bad about these lies because he is not able to apply the term heroic to anything that happened. The people in his hometown cling to old ideas about the glory of war. Krebs cannot relate to them. He has been changed by the war, but nothing has changed in the town:
Nothing was changed in the town except that the young girls had grown up. But they lived in such a complicated world of already defined alliances and shifting feuds that Krebs did not feel the energy or the courage to break into it.
The former marine, who had fought at Belleau Wood, is lost in this world he no longer understands. He lacks the wherewithal to fit into this milieu. And, even though he says he will go to Kansas City to get a job, the reader is left with the impression he has no home. He does not fit into the old life and ways of America. Not surprisingly, both Hemingway, and his character Jake Barnes, leave America in the 1920's to return to Europe because they felt, like Krebs, alienated from an America they could not relate to.