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So, communism and fascism are both on the left,

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That is a fatuous argument and it is historically inaccurate.

That elements are shared in common by 'isms' does not make them functionally the same or place them on the same side of the political spectrum.

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Fascism /ˈfæʃɪzəm/ is a form of radical authoritarian nationalism,[1][2] characterized by dictatorial power, forcible suppression of opposition, and control of industry and commerce,[3] that came to prominence in early 20th-century Europe. The first fascist movements emerged in Italy during World War I, before it spread to other European countries. Opposed to liberalism, Marxism, and anarchism, fascism is usually placed on the far-right within the traditional left–right spectrum.[4][5]

Since the end of World War II in 1945, few parties have openly described themselves as fascist, and the term is instead now usually used pejoratively by political opponents. The descriptions neo-fascist or post-fascist are sometimes applied more formally to describe parties of the far right with ideologies similar to, or rooted in, 20th century fascist movements.[14]

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