Not being a Fascist, I cannot speak authoritatively for Fascism.
However, National Socialism is a subject of the same debate: is it leftwing (as the Right charges) or is it rightwing (as the Left charges)?
Here is the way that my old friend and comrade Matt Koehl put it:
"The Old Order has its leftwing and its rightwing. But we National Socialists are not part of the Old Order. Consequently, we are not part of either its leftwing or its rightwing. Rather, we represent a resurgent New Order for Aryan humanity, and as such we transcend the traditional Left/Right dichotomy."
That is the best way to understand it, rather than trying to cram either National Socialism or Fascism into some ideological pigeonhole in which is does not fit.