This is from wikepedia as well:

"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]"

"Usually placed on the far right"...etc.

The left and the right can keep calling each other fascists but the current reality is a bit more nuanced than that and untrue.  I had this same argument with somebody a couple of months ago.  

That being said, Neo-Nazis take pride in their fascism and happily make this claim - the rise of the AntiFa (anti-fascists).  All pretty stupid in the end if you ask me.