I think you are misplacing Hitler... he is nowhere near you and Ghandi.
It's probably, in part, because you have been fooled by the word "socialist" in the "National Socialist German Workers' Party" (aka the Nazis).
However, as you well know, just because a word is in the name of a political party (or a country) it does not mean that is what the party (or country) actually is. The "Democratic People's Republic of Korea" is a prime example, which I am sure you don't need for me to explain to you.
Yes, the Nazis had a limited few socialist like policies. They were not, however, even close to being true socialists. Hitler and his regime were center-right authoritarian
I'm sure you will disagree, but your disagreement is just your tendency to play the devils advocate.
Left and right are of limited value at the best of times, but of no value whatsoever when people claim Nazism and fascism are on the right. I understand why academics (who tend toward the left) are all desperate to demonise these two ideas and call them right wing - it deflects from the fact that the most murderous people in history are predominantly on the left, and allows them to pretend that Marxism is not authoritarian in its ideological conception and brutally despotic in practice.
When you have no choice but to claim Stalin, Pol Pot, Ho, Mao etc., I guess you want to palm off anyone else you can. Reaching 100,000,000 dead people in less than 100 years last century (the all time record for ideological killing by the way - it took Islam a few centuries), is bad enough. Adding a world war to it, and
fascism? Not even the leftists could bear that. So, they lie.
What makes Nazism right wing? Is it the nationalist element? No.
The current state of "Communist" China is a lot like Nazism, only further to the right in terms of it's economically liberal policies (in that it allows non-national interests to participate). And in the past Communist China and the Soviet Union fought over their respective national interest. And as any of us who are over the age of 30 know damned well, trade labour unions in the west were once very nationalistic and openly placed their own workers above the global proletarian movement. So the lie that nationalism has no home on the left is absurd.
As I have said here before, I am not on the right. That does not mean I will suck the lefty propagandists teat though.
wanted government control of education (sounds like SJWs to me).
wanted government control of healthcare (sounds like SJWs to me).
wanted government control of the economy (sounds like SJWs to me).
placed the common good above the individual (sounds like SJWs to me).
believed one race was privileged (sounds like SJWs to me).
called for "social justice" against the privileged race (sounds like SJWs to me).
advocated the silencing of dissent (sounds like SJWs to me).
used violence against dissenters (sounds like SJWs to me).
wanted to eradicate ideas (sounds like SJWs to me).
Are the SJW/"Progressive"/"Democratic Socialists" on the left or right? They have a lot in common with Nazis.