Please describe someone who could be considered neither left nor right. Is it possible you are viewing the absence of left-wing qualities as being right-wing?
Exactly. So I am curious why OP considers it remarkable that "neither left nor right" is not what it seems.
As for me, I might consider someone from a different country with different politics, like Japan perhaps, to be neither. Or someone who lives under a rock and doesn't pay attention to the news.