Put simply, the angel Michael disobeys God because the woman pleads with Michael to allow her to live so that she can care for her babies.
In his late works, Tolstoy's intention was chiefly to write parables with a religious message, preaching self-denial and compassion for others while demonstrating the uselessness of worldly possessions and money. In "What Men Live By," the shoemaker, Simon, is ultimately rewarded for his sacrifice of giving his coat to the naked Michael when he first encounters him outside the shrine. Michael himself, when he ultimately explains why God banished him to earth, is revealing that his own behavior in disobeying God encapsulated the principle that men "do not know what they need." When Michael initially doesn't take the woman's soul, allowing her to go on living however briefly, the result is that the woman rolls over onto one of her babies and crushes its leg. Michael is therefore guilty, just like mortal humans, of not understanding what was required at the time—and also of not realizing that someone else would adopt the babies even if their mother's soul were to leave earth.
The transience of earthly life, in this story and in other late works by Tolstoy such as "Master and Man" and "How Much Land does a Man Need," is a central theme. Tolstoy himself, well after his reputation has been established by War and Peace and Anna Karenina, seemed to be aiming for a new type of didactic writing, stripped of non-essentials and devoted to imparting a religious message. "What Men Live By" is perhaps the "purest" of these later works, with its biblical imagery and austere tone.