Hitler was the initiator, the decider. There was an idea underlying his decision. He did not act upon some vague concept of "anti-Semitism." Hitler was a thinker.

As mass-murder gained momentum in mid-1942, Hitler claimed to be undisturbed by the murder of men, women, and children:

If I don’t mind sending the pick of the German people into the hell of war without the slightest regret over the spilling of precious German blood, then I naturally also have the right to eliminate millions of an inferior race that multiplies like vermin (Meltzer, 1991).

Hitler recognized that he--as national leader--was permitted to send millions of his own soldiers to die in warfare. No one objects when a national leader sends soldiers to die on the field of battle. 

Hitler understood that nations have the right to kill. If national leaders have the right to send their own soldiers to their deaths, he reflected, why should a national leader spare the lives of their mortal enemies?

The logic of genocide followed based on the logic of warfare. Nations have the right to kill.