At what point did I deny any of this?

By your system of definitions, Hitler was right wing and Stalin was left wing, yet functionally they were identical. Is it so hard to believe that in the eyes of some they may both be considered to be on the same side of the political spectrum?

These pereceptions and definitions are not set in stone, they have evolved over time. Treating them as if they are absolute, because they are not.

In order to argue logically (vice emotionally) you must establish your definitions and assumptions at the outset.