Hitler explained his thinking or logic that led to the Holocaust quite clearly (see box below). He understood what many historians do not understand: That in war, leaders of a nation have no problem sending their own soldiers to their deaths. This is their "right."
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Hitler extended this understanding of warfare or battle. If he had "the right" to kill (sacrifice) his own soldiers, would he not also have the right to kill millions of an inferior race; mortal enemies of the German people?

Beginning with recognizing--that Nations have the Right to Kill  (to sacrifice their own soldiers)--one can understand the grotesque logic that led to the Final Solution. If Hitler--"without regret"--didn't mind sending his own soldiers (the "pick of the German people") to shed precious blood,  why would he have any regrets about eliminating millions of an inferior race?

Hitler's thinking in mid-1942 as the Holocaust began with the shooting of Jews by the Einsatzgruppen:

"Nature if cruel. Therefore, we too may be cruel. If I don’t mind sending the pick of the German people into the hell of war without the slightest regret over the shedding of precious
German blood, then I naturally have the right to eliminate
millions of men of an inferior race that multiplies like vermin (Meltzer, 1976)."