Socialism was prevalent in Germany and hitlers selection of national socialism was specific to delineate his group from much of socialism in germany which he considered Jewish. Fascism or fascismo means 'group' in Italian. The american thinker is pro-individual. Mussolini considered himself a socialist, the quotes are there. Hitler modeled fascism into nazism. Also, there are many other quotes from hitler and his contemporaries stating that they are socialist. You also need to look at the 25 point plan. It is very anti-individual, anti-capitalist, centralized government, anti-democratic, anti-parliamentary, and very statist in its policies. That is not right winged. Some of the militarism and nationalism are definitely right winged. Rohm the head of the SA was a self proclaimed socialist, but he was also a militarist, so a union of both wings of politics. He was also gay, and once Rohm became a threat and his behavior fell out of favor with the nazi ideal, he was vanquished. Also, perspective is warranted. Liberalism and conservatism in Germany 1938 is nothing like the american democrat or republican.
Note, that many rightly state that the more conservative business elite in Germany joined ranks with Hitler. But why. The truth of the matter was the communists had won a large portion of the elections and they feared the communists more for their own welfare, and in their own self interests they joined the nazi party. If not, why did they not join earlier in hitlers rise. Some causality that's always omitted.
Also, the fact that academia immediately spouts nazism as right winged should be looked at with biased eyes. What percent of teachers in today's or yesterday's universities are truly left winged. About 90%! So why would teachers from the last 30 years declare nazism as left winged. It's not going to happen.
Anybody with honesty can see that hitler used everyone, including his own people, his own supporters, et. al. He picked the Christian socialists for the 'heil hitler', the deaths head from the Prussian military, etc.
Nazism is a mixture of both left winged and right winged ideology if you have any intellectual honesty. Read his policies before he took authoritarian rule. Hating Jews does not make it right winged, and stating or thinking so just makes you just another lemming fanatic.
Also, look at Wikipedia under socialism. Every instance of racist socialism is removed and labeled separately as right winged. Why? Because it plays into today's american politics. Today Europe is still heavily anti-Semitic but it is almost entirely socialist in politics. It's an amazing numerical coincidence that all those anti-Semites are the vastly right winged minority in Europe. I think not. Be honest and think for yourselves.
Nazism is a mesh of everything hitler could use for himself be it from the volk, the business elite, the militarists, the nationalists, the socialists, the racists, the Christians and Catholics, the pagan, the social Darwinists, the ecological purists, etc.