In school, I was taught that fascism was not in fact right wing, but compared to American Government, it was very much left wing. Our history class taught that the Nazi party of Germany had a meeting with the Communist Party of Germany to discuss a number of things starting on what slogans would be and what category they would say they were. Fascists were very much left wing, but they looked like right wing extremists compared to the communists, so they decided to call the communists left wing and call the fascists right wing to avoid confusion.
Fascism is left wing because you cannot own a business or large home if you don't toe the line that the ruling party draws.. If you don't toe the line, they take your business and give it to someone who will. It is far right of either communism or socialism in that it allows private property at all. In socialism the government owns all the business and makes sure that everyone is paid equally, and in communism the gov't owns everything and makes sure that everyone has everything they need.
So fascism is far right of communism but still pretty far left of American conservatism. It's somewhere in the middle.