It's not illogical.

Some losers become Nazis, because having a scapegoat feels good and doesn't require you to do any thinking or self-improvement. Many losers also cannot get laid because they are insufferable twats. Often, these things are related.

The AI waifu loser nazis simply assume that the chads they have been told exist will have all the babies and make a new generation of super alphas.

They also assume, wrongly, that, if this were to somehow happen, they would not also get turned into gristle for the wheels of fascism under some pretense.