That is a fallacy that was created by the Progressives when WWII broke out. Yes, Nazis are socialists. They were always socialists. Look at what the Nazi party stood for and then tell me they are far right. Do a search for the 1928 Nazi party platform.
Mussolini didn't jump to the far right. Look up Giovanni Gentile and find out what he did with socialism.
You can deny it all you want but the fact remains Nazism and fascists are just another variation of socialism. Just like Marx's communism.
The American Progressives in the early 20th century used to praise Stalin, Mussolini and Hitler. They called them the "the men of the future". But when WWII broke out and we went to war with nazis and fascists then the Progressives dumped them like a hot potato and did what leftists always do, accused the right of being nazis and fascists.
Because most of the newspapers and most of the college professors at that time were Progressives it wasn't hard for that idiotic scale that put nazis and fascists on the far right to get pushed into the heads of people who never thought it through.
Socialism and the 3 other ideologies that are based on socialism, communism, fascism and nazism all have the same foundation. The elimination of private property rights, the government controls the means of production. Wealth is redistributed so that all are equal. They all incorporate the labor theory of the cost of goods. And the individual is stripped of all rights.
If you divide two of those groups on the right and the other two on the left then were is there room for freedom. There is none.
The proper scale is to put all of those authoritarian forms of socialism along with monarchies and any other kind of dictators/oligarchs all on the far left. The far right is anarchy, true anarchy. There are a whole lot of people claiming to be anarchists but their entire purpose is to destroy an existing government with anarchy and then replace the the government with, typically, communism.
No I am talking about people who do not want any government at all. They don't want to replace one government with another. Those people are at the far right.
Just to the left of true anarchists are the Libertarian Party. Just to the left of the Libertarians are the founding fathers and the Constitution Party. A little to the left of the founding fathers are Republicans.
Way over on the far left is the Democrat Party. They may or may not be to the right of the authoritarians.