Not the person you were replying to but there's this strange idea amongst alt-right folks that Nazis were socialists because the party called itself the National Socialist party. Could be referring to that.
The Germans had a term for communists who swapped to the Nazi party - Beefsteak Nazis[4]. Brown on the outside and red on the inside.
1. https://en.wikipedia.org/wiki/Strasserism
2. https://en.wikipedia.org/wiki/Ernst_R%C3%B6hm
Seriously, it's not difficult to understand that any majorly autocratic government, left or right, needs a centralized government by definition.
That is got nothing to do with being left or right, but with being liberal or autocratic.
Note I say ideas here, because the reality is e.g. the republicans in the US are for the most part big government politicans despite being on the right, but that seems more a bastardization of the traditional right, which historically is about smaller government.
So generally speaking, because left wing political ideas tend to involve big government, it means that centralization is generally more extensive in left wing governments, and I would argue thus left wing governments are more liable to be autocratic.
"Various work programs designed to establish full-employment for the German population were instituted once the Nazis seized full national power. Hitler encouraged nationally supported projects like the construction of the Autobahn highway system, the introduction of an affordable people's car (Volkswagen) and later the Nazis bolstered the economy through the business and employment generated by military rearmament. The Nazis benefited early in the regime's existence from the first post–Depression economic upswing, and this combined with their public works projects, job-procurement program and subsidised home repair program reduced unemployment by as much as 40 percent in one year. ... Upon being appointed Chancellor in 1933, Hitler promised measures to increase employment, protect the German currency, and promote recovery from the Great Depression. These included an agrarian settlement program, labor service, and a guarantee to maintain health care and pensions."
Of course, you could say that Republicans in the United States have also done some of these things, but again, that would be Socialism on the right.
Vox has a pretty good explainer of the differences between Hitler's National Socialism and socialism. https://www.vox.com/2019/3/27/18283879/nazism-socialism-hitl...