Fascism and Nazism are both right wing ideologies.
Discussion
It's worth remembering the context of where right and left arose: the French revolution.
Nobody was pushing individual liberties and free market capitalism.
The words "Fascism" and "nazism," and "socialism" and "communism" "marxism", "leninism" and "capitalism" were around before we thought in term of left/right thinking. Its an example of gross simplicity fallacy.
We need to get back to definition of terms. Leave right/left behind and let's talk philosophy. Most of the "isms" are just a rebranding of older ideas mean to enslave us. With the exception of Individualism. Individual freedom is antithetical to both the current right, and left.