When Elie's father is forced to stay in the camp for a "decisive selection," he hands his son a knife and spoon. Weisel refers to this as "the inheritance." What is the significance of the word choice?
There are two "word choices" in your question: the choice of "the inheritance" and the choice of "decisive selection." Since "the inheritance" is Wiesel's means of describing events surrounding his father's retention in the camp for "decisive selection" and his father's subsequent and directly related action of handing Elie his knife and spoon (Elie already has his own knife and spoon), the word choice "the inheritance" seems to be the more comprehensive and thus the more important of the two.
"Inheritance" can refer to qualities you gain from your parents at your birth, but birth doesn't fit the context of "decisive selection." "Inheritance" also, and more importantly, means property you receive from your parents (or other relative or friend) after their deaths: inheritance is set out in wills, which are read out to heirs after the writer of the will--father, mother, aunt, etc--has been laid to eternal rest during their funeral.
Elie, like all the experienced internees, knows what happens in the camps for "decisive selection": if you are still fit and can work, you are selected for labor, but if you are not fit or are old or ill, you are left behind and selected for death. Elie's father's name appears on a list of persons selected for death. The father knows that these are his last moments with his son and, in his attempt to say and do all the things he must say and do before leaving this earthly life, he hands his knife and spoon to Elie.
The knife and spoon are all that he possesses and they constitute the whole of the inheritance he can hand down to Elie. Yet, since he knows his death is imminent and since he knows Elie will soon be taken from him forever, he can't wait until after his death: he gives Elie his inheritance now, while both are still alive and breathing. The significance of the word choice "the inheritance" is that both father and son know that they must part immediately and that the father will die equally immediately: what would be given by others after burial exchanges warm hands between the fully knowledgeable soon-to-be-dead and the yet-living.
Wiesel's word choice in describing the "decisive selection" is a way to communicate the terrible condition of life in the death camps.
At this point in the narrative, Wiesel has established the terror that is such a part of the Holocaust. Terms like "selection" and "indifference" help to define this reality. Wiesel has described an inverted world. It is one where nothing seems to make sense. The worst of crimes is done with a striking banality, as if it is no big deal. The idea of "selection" is twisted in how it is meant to choose who lives and who dies. In this world, Wiesel precisely uses language to communicate horror at the lack of order.
It makes sense that this world is one where fathers and mothers cannot provide for their children. The traditional order has been inverted. At the moment of a "decisive selection," such an existence is amplified through Wiesel's word choice. Wiesel's father is afraid that "time was running out." The "rapid" and "confused" speech conveys the extent to which the world of the death camps defies traditional custom. In other words, the way that Wiesel describes Eliezer's father shows how distorted things are in the Holocaust. This is underscored when Wiesel describes how the father gives the son his "inheritance." Traditionally, an inheritance is a grand event and accompanied by elaborate displays. However, in the world of Auschwitz, the father gives the son a spoon and knife. When Eliezer's father insists that the son "take what I give you," it indicates that while he wishes to give his son so much more as an "inheritance," the Holocaust has robbed this from him. Parents are no longer able to do their duty to their children. The description of Eliezer's father as having "tired eyes, veiled by despair" shows the destruction of sacred and traditional bonds between parents and children is one of the true terrors of the Holocaust.