Section 22 pages 270-end Q 5

THe father refuses to have his son die in his arms. His whole being was to keep his son alive regardless of the Hell this world had become. The father simply did not have it in him to kill his own son, even if killing him was the responsible thing to do. 

The father can’t kill his son because he would be abandoning his beliefs that he has been carrying throughout the entire novel, which has been to keep his son alive.