They were, but limited it to the nation. Nazi means national socialism

The word socialist here isn't akin to socialism as we know it in the traditional sense. People use it to support their use of the "socialism" scare-word.

It's like how governments will call themselves "democratic republic of" when they are neither democratic nor a republic.

We have to be careful around terminology in these discussions because it is very easy to fall into logical traps and speak as if we are on different sides of a topic when we probably actually agree.

Bottom line is we should always be wary of "strong men" who promise the salt of the earth ordinary joes to "finally get what they deserve" or restore their former glory after being downtrodden by the "other". It doesn't matter what clothes the emperor is wearing, always ends up the same.