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One paved the way for the other.
They didn’t start out with extermination on day one. Before that they failed an attempted coup, stripped Jews of their rights, forced the emigration and deportation of Jews, and had to build up the capacity of the future death camps.
Their point is to recognize the rise of fascist authoritarianism before we’ve reached the holocaust stage.
I wouldn’t minimize the comparability when there are such blatant examples of Trump utilizing Nazi propaganda like the Big Lie and the demonization of an out-group, like the Nazi’s antisemitic populism, to gain power.
Prior the Reichstag fire, the Nazi’s electoral high point was 37% in 1932 (or 31% of Germans at 82% turnout), compared with Trump at 49.8% last year (or 31.8% of Americans at 64% turnout). The point being that you don’t need a significant buy-in from the people to elevate leaders with dictatorial motives. You simply need a triggering event which they can use to justify their consolidation of power permanently.
Also, if the desire is to avoid authoritarian leadership, I’m not sure military coup is the play. I know the American Armed Forces swear an oath to uphold the Constitution, but it seems that would get real tricky once you’ve overthrown the Commander in Chief, in defiance of the Constitutionally mandated chain of command.