Was Hitler a socialist? Is there any policy to support the claim Hitler was Left-wing?

In the most basic terms socialism is the belief that society shouldn't have any hierarchies. People are all atleast naturally equal, nothing makes one person worth more than the other, not his noble heritage, his fathers wealth or anything else. Any society that has some people on the top and a few on the bottom is therefore an unfair society.

Fascism is kinda the opposite. Some people are naturally better than others, therefore it is best if the good people get to the top society, while the worse people fall to the bottom. Infact this is good for everybody they argue, because a society of strong people led by weak ones is bad for the entire society. So fascist want to reinforce hierarchies and believe them to be good, and the ultimate hierarchy is the nation, with the leader on top and people in the bottom. Nazism and Hitler expanded on this by adding race as another hierarchy.

Hitler despised socialists and communists, even labeling them as a seperate race that needed to be wiped out. But there are two reasons one might mistake fascism and nazism for socialism. The founder of fascism, Mussolini was initially a socialist who eventually got fed up with socialists and created fascism so some might think fascism is an offshoot of socialism but it really isn't. The other reason is that Hitler, ever the shrewd politician, labeled his ideology national socialism and incorporated some socialist ideas early on to attract left wing extremists to his party. These extremists formed the basis for the SA, the military arm of his party. Once he came into power though he quickly got rid of the SA and never really enacted any real socialist policies.

The economic policies of Hitler were focused on the state, all industries and companies exist only to serve the state. There was some nationalisation of industries and imports/exports were limited. At the same time however Hitler was quite pro-business, as the idea of companies competing and forcing inferior competition out of business was close to the social darwinism of fascism. The economic model of nazi germany doesn't really fit the box of market economic and planned socialist economies but it wasn't really socialist as the point was never to allow the workers to "seize the means of production".

Some groups today use the misconception, usually far right groups, to blame the holocaust on the political left while at the same time paint themselves as non-nazis and as opposing the nazis. It's basically a PR move founded on historical revision.