The Nazis did not "gravitate first to socialism." When the Nazis first formed they were a loose collection of non-establishment types, including socialists. As time went on and they gained political power, there was a struggle internally whether to strive for socialist ideals. The socialists lost and nearly all of the socialists in the Nazi party paid with their lives, as the Rechtsextremistenen didn't want their rivals alive to potentially take revenge and power later.

Read some history. This is all well documented.