Harris acknowledged at the time that if the Nazis had won the war, they would have executed him as a war criminal. That doesn't mean that he believed that he was one.
In fighting such a war, the important thing is to win it, because the winners decided what was acceptable and what wasn't. Broadly speaking, the moral justification for Allied actions was that Nazi Germany represented such evil that almost anything to put an end to the regime was justified. Naturally, the Nazis didn't see it that way...
It may not often happen in wars, but if ever there was a case of one side being clearly and totally in the wrong, in terms of both starting the war and in their behaviour during it, the Nazis qualify. As indeed do the Japanese, but that's another argument - and no-one seems to get too fussed about the firebombing of Japanese cities.
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