I understand and agree with your point that the arrogance is both their motivation and downfall, I just don’t agree that it should be phrased as arrogance causing their defeat itself.

The Nazis weren’t beaten because they were arrogant. The people they hurt and tried to hurt have their own agency, and it was their choices and actions that beat the Nazis.

That’s important. It takes deliberate effort to beat fascism, from everyone opposed to it.