I agree, but there is even more to this part. The Nazi ideology was not just about superiority, about also about struggle between races for power and need to win that struggle. You have to fight for your own and prove superiority through military conquest and physical domination of other races.
For that to happen, you need certain kind of fighter. Ruthlessness and nazi really seen ruthlessness as virtue.
Empathetic male eager to share emotions is less likely to gain domination through violence. Or through manipulation, backstabbing, lying and all those things that are seen as practical tactic by white supremacists. Less likely to push knowingly for laws that harm minorities or political opponents. Less likely beat or kill opponent. Less likely to force own friends into compliance with own ideas.
By that I want to say that the aggressive masculinity is virtue and something you want males to be, if you have aggressive goals. Hence peer pressuring males to be like that.