::::::Except, of course, that the Nazis were not socialist and no reliable, mainstream source labels them as such. Read it again: "In advanced liberal democracies, perhaps more than anything else the right has been defined in opposition to socialism or social democracy." In other words, liberal democracies today define left and right in this way. The definition goes on to state that right wing includes "...nationalism; and for extreme-right parties racism and fascism." The Nazis were nationalistic, racist and fascist, thus extreme right-wing. This is what the sources say so this is what we use.