But that's not the same as fascism is left-wing or? As your right of course but I'm not arguing against that but the notion that either fascism or nazism is left-wing. If that's the case, communism is right-wing and the whole system collapse
Both extremist sides have many things in common but we don't define them in the whole "right-wing left wing" scale based on that, (we simply call them authoritarian/undemocratic etc etc. We tend to lump them together on their differences, which I admit can be hard to define but it's there, and it's also based on their own stances. Ie, the two extremes didn't like each other, despite being somewhat similar, like the "original" nazists being lumped together with other right-wing extremists () because they cooperated against the communists.