The NSDAP began as a socialist and nationalist movement when it was founded by Anton Dexler. In order to win the support of the aristocracy, the bankers, the military, and the industrialists, Hitler eliminated the economic radicals from his party during the Night of Long Knives. With people like Roehm and Strasser out of the picture, the NSDAP was "socialist" in name only. No property (other than Jewish property) was nationalized, the banks stayed in private hands, and the aristocracy held on to their land.
Similarly, the fact that Mussolini began as a communist doesn't prove much about your point either, plenty of the most militant anti-communists started out as leftists in their youth.
Your argument basically boils down to the idea that fascism isnt communism and therefore hitler was right wing.
A lot of leftist a make that point.
communism and socialism and fascism are all on the left, they are nearly identical.