Fascism was left wing as it was invented by Mussolini. Mussolini was remarkable in that he was one of the few revolutionaries of the time who did not mass murder millions of his own people. In fact, his rise to power went astonishingly smoothly and quickly. He committed the targeted killings of some people, but nowhere near on the same scale as Stalin and Hitler did.
This make Stalin intensely jealous, because fascism was working much better than the long hard bloody fight Stalin went through to achieve his own power. Stalin immediately branded Mussolini as right wing, mainly out of jealously over how much better fascism was working as compared to Stalinism.
Stalin called it right wing because it simply made the existing capitalist owners of the means of production into members of the fascist government, thus accomplishing the nationalization of the means of production without having to confiscate the means of production from its capitalist owners, as Stalin did. Giving the capitalists a high government title and a government paycheck won them over much more quickly than a bloody revolution.
This enraged Stalin, and he said that perpetuating the existing capitalist ownership was right wing.
Really, it was left wing propaganda. By definition, fascism was as left wing as anything Stalin was doing. It was just working much better under Mussolini's leadership.
When Hitler came along, he took the parts of fascism and Stalinsm that seemed to be working the best, and he called it National Socialism. Of course, taking parts from two left wing systems results in another left wing system.