I would first ask you how communism was NOT "statist authoritarianism."
I have a rather different take on how fascism came to be viewed as being rightwing.
Part of the problem in recognizing fascism has been the assumption that it is conservative. Zeev Sternhall (in "Fascist Ideology" in Fascism: A Reader's Guide, pg 316) observed how the study of fascist ideology has been obscured by "the official Marxist interpretation of fascism." The Marxists defined fascism as their polar opposite. If Marxism is progressivism, fascism became conservatism; If Marxism is leftwing, fascism became rightwing; if Marxism championed the proletariat, fascism championed the bourgeoisie; if Marxism is socialist, fascism became capitalist. The massive influence of Marxist scholarship (to this day Western universities continue to be dominated by Marxist thought) severely distorted the understanding of fascism.
But the fact remains, Marxism and fascism were both rival brands of the same thing (socialism). Where Marxist socialism is predicated on an international class struggle, fascist socialism promoted a socialism centered in national unity. Both communism and fascism opposed the bourgeoisie (remember "German WORKERS' Party." BOTH attacked the conservatives and destroyed them. Both were mass movements, which had special appeal for the intelligentsia, students, artists, workers - the normal leftist groups. Both demanded strong, centralized governments and rejected a free economy and the ideas and ideals of individual liberty.
When you study the history of American progressivism, you find they were HUGELY supportive of fascism until Stalin literally gave them different marching orders. Many of the top progressives of the 1920s and well into the 1930s were huge Mussolini and Hitler fans. American progressives went to Italy and particularly Germany to study this "wonderful" new form of government.
It is very easy to understand Theodore Roosevelt as a fascist-style progressive.
Well said.