The main conflict in the play "All My Sons" is over the sale of defective parts to airplane manufacturers by Keller's company. Those parts were used in planes that crashed at war, killing the men onboard. Larry Keller was so distraught over the thought that his father had knowingly risked other men's lives that he could not live with himself. When Mrs. Keller says that God would not allow a father to kill his own son, she is both defending her husband and denying her son's death. Larry has not been declared dead; he is listed as missing in action. So her denial lets her continue to believe the best of her husband and her son.
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This is the root of Kate's denial. She cannot face this reality, so she has set it up as some sort of cosmic rule. Of course, we know that sons can be killed by fathers, and that it happens not uncommonly. But, what she is saying is that Larry could not have been killed by Joe. That is what she cannot face. How could she continue to live with Joe if that were the truth? How could she continue to live in a home supported by the money made by that company?