The debate, such as it was, was mostly in the 1920s, before the fascists had accumulated enough power to carry out these atrocities. Partly, there was the simple problem of describing a new political form. Fascism was a new and distinct form of reaction; fascists weren’t monarchists, for instance. Part of it was that there were a few more-or-less left groups that were short on theoretical clarity and long on opportunism, so a few such groups initially expressed admiration for some aspects of fascism, before they realized they were near the top of the “kill” list. Also, then as now, there were also those who insisted that socialism simply meant state control of the economy, without regard to who controlled the state and how.
Partly, this gets into how one defines “left” and “right”. If you think “left” means favoring the redistribution of power to the disenfranchised to achieve social equity, and “right” means favoring the concentration of power in an elite, then clearly fascists are on the right. If think that “left” means concentration of power in the state, then you can see why someone might think fascists are “left”. And, if you think “left” means opposition to tradition, and “right” means reinforcing tradition, then fascists are damned confusing.
Historically, I think the first definition is the one with the strongest grounding and the most continuity and consistency. But it is, after all, a metaphor.
