From They Thought They Were Free: The Germans 1933 - 1945, in which the author Milton Mayer got to know and interviewed 10 Nazis (the mentioned "friends") about the rise of fascism:

Because the mass movement of Nazism was nonintellectual in the beginning, when it was only practice, it had to be anti- intellectual before it could be theoretical. What Mussolini’s official philosopher, Giovanni Gentile, said of Fascism could have been better said of Nazi theory: “We think with our blood.” Expertness in thinking, exemplified by the professor, by the high- school teacher, and even by the grammar- school teacher in the village, had to deny the Nazi views of history, economics, literature, art, philosophy, politics, biology, and education itself. Thus Nazism, as it proceeded from practice to theory, had to deny expertness in thinking and then (this second process was never completed), in order to fill the vacuum, had to establish expert thinking of its own— that is, to find men of inferior or irresponsible caliber whose views conformed dishonestly or, worse yet, honestly to the Party line. The nonpolitical pastor satisfied Nazi requirements by being nonpolitical. But the nonpolitical schoolmaster was, by the very virtue of being nonpolitical, a dangerous man from the first. He himself would not rebel, nor would he, if he could help it, teach rebellion; but he could not help being dangerous— not if he went on teaching what was true. In order to be a theory and not just a practice, National Socialism required the destruction of academic independence. In the years of its rise the movement little by little brought the community’s attitude toward the teacher around from respect and envy to resentment, from trust and fear to suspicion. The development seems to have been inherent; it needed no planning and had none. As the Nazi emphasis on nonintellectual virtues (patriotism, loyalty, duty, purity, labor, simplicity, “blood,” “folk- ishness”) seeped through Germany, elevating the self- esteem of the “little man,” the academic profession was pushed from the very center to the very periphery of society. Germany was preparing to cut its own head off. By 1933 at least five of my ten friends (and I think six or seven) looked upon “intellectuals” as unreliable and, among these unreliables, upon the academics as the most insidiously situated.

Anti-intellectualism isn't the only ingredient, but it's one of the most important. It's a reactionary movement that injects hate into people's hearts in order to consolidate power for the privileged. Those "little men" who support the regime feel that they were elevated above the people whom they hate, and were often the beneficiaries of the cruel treatment and dispossession of the victims.