Fascism and (especially) Nazism were essentially a reversion to pre-Christian ideals, while Communism was a heretical perversion of Christian ideals themselves.
Our word virtue and our word virility are both descended from the Latin for “man.”
To the ancients, these both meant manliness, which they saw as the highest good. But their idea of a real man was largely what we would think of as a bully, the dominator of others, the conqueror.
Christ provided a contending idea of what a real man is or should be. It was so foreign to the thought of the time that even his own followers didn’t really comprehend it till after his death.
The two ideas of manliness have fought it out ever since in western civilization. Chivalry was only one of many attempts to reconcile the two.
Fascism rejected the Christian ideal and reverted to the ancient pre-Christian notion. Just about everything in what Fascism stood for flowed from that.
This is as opposed to Islam, where the ideal of manliness as domination was never challenged. It was, in fact, reinforced by the example of Mohammed.
“Virtus” in Latin does not mean “virtue” in the sense we use today, but “valour” as in military prowess.
I’ve translated enough Latin in my Italian “Liceo Classico” secondary school to know that.