I never could understand why the Nazis were considered as an extreme right wing organization and the Communist Party is an extreme left wing group.
Because lib professor-types were the ones making up the definitions.
It had to do with where they sat in the Reichstag.
The answer is very simple: from the 1920's until the fall of the Soviet Union, "left wing" meant supportive of the goals of the Comintern, "right wing" meant opposed to the goals of the Comintern. Thus, Tories, Republicans, Nazis, monarchists, fascists, Democrat Cold Warriors, Christian Democrats, classical liberals, nationalists of just about any description, were (and by linguistic inertia still are) called "right wing", while Labourites, Democrat pacifists, Communists, socialists, social democrats (esp. of the "nuclear freeze" supporting type), etc. were and are called "left wing".
Because the left said that's the way it is and because the left controls the media and intelligencia, they can get away with it.
stalin insisted on the national socialists being labeled “right”
to distinguish them from the communists on the left.