Krebs decides to leave home because he can no longer relate to the people around him. This is an all-too-common experience among war veterans. Krebs witnessed a lot of death and suffering at first hand while serving at the front, and his experiences have changed him forever.
Among other things, this means that he feels isolated from those around him in his home town. They haven't had the same experiences as him; they can't begin to comprehend the sheer scale of the horror that Krebs was forced to witness on a daily basis. So they can't understand what he's going through.
For all the deep trauma he suffered at the front, Krebs was at least able to develop a sense of camaraderie with his fellow soldiers. But such a sense of solidarity is completely unavailable in his home town. The townsfolk are simply not interested in the terrible truth about conflict; they'd much rather hear romantic lies and fabrications about the alleged glory of war. But Krebs is sick of lying, and his decision to leave home can be seen as an unequivocal declaration of his fidelity to the truth.