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I feel like it's rather stupid to simplify everyone into 2 big groups. Am I far right?
This isn't simplifying people into 2 big groups, it's talking about 2 big groups among many, many, many groups.
Isn't the image implying that people who says they are not left or right are actually far right?
No, it's saying that far-right people claim they aren't right or left, and just care about the truth, as a means to distance their image from their actual views.
Some people genuinely aren't left or right, those people are generally Social Democrats, ie Capitalism with strong social safety nets and some level of government ownership of some key industries. However, this isn't perceived as being a centrist view due to the Overton Window, ie in America, Liberalism, a right wing ideology, is the status quo, with a liberal party and a fascist party.
The logic chain is a bit different.