As German Soldiers were required to die in battle, so Jews would be required to die in gas chambers
Richard A. Koenigsberg

The logic of genocide followed the logic of warfare.

 War is the occasion in which soldiers are obligated to die for a nation-state. Why should Jews be exempt from such an obligation?

As German soldiers died at the behest of the German nation, so Jews would be required to do the same. The Holocaust was a degraded or debased version of "dying for a country:" Death at the hands of a nation-state with words like "honor" and "glory" subtracted. 

Hitler's statement below foreshadows the Final Solution:

Hitler (Mein Kampf, 1924): “If at the beginning of the War and during the War twelve or fifteen thousand of these Hebrew corrupters of the people had been held under poison gas, as happened to hundreds of thousands of our very best German workers in the field, the sacrifice of millions at the front would not have been in vain.”

If German soldiers had died in the First World War, so Jews should have died as well. If German soldiers had been killed by poison gas attacks," so Jews too should have been “held under” poison gas.

The logic of genocide followed the logic of warfare. Warfare is the occasion in which soldiers perform the “work” of dying for a nation-state.

 Why should Jews be exempt from the work of dying? As German soldiers died at the behest of Germany in the First World War, so Jews would be required to do the same. The Holocaust replicated the First World War, Jews substituting for German soldiers.