One example is the economic metric, which is most obviously flawed by viewing 'centrists'. 'Centre' should be a 50/50, exactly between left/right.

Extreme Economic Left - everything is fully state owned, no private property exists.

Exetreme Economic Right - nothing is state owned, only private property exists.

Centre on the graph is located exactly between extreme left/right (this represents 'centrists'), therefore should represent individuals that believe in a 50:50 state owned/private property and economy. Ie through two extreme opposing views or two centre views etc.

But... How many 'centrists' by the Political Compass metric believe 50% of property rights and/or economy should be state-owned?... None.

Why does this matter? Unfortunately, PC has become the most common categorisation of political beliefs. And this categorisation represents a major (biased) frame shift along the X-axis toward right-wing economics. Where 'right-wing' becomes centrist (or normal): mild left positions look more extreme, right positions look less extreme.

Wondering why Hitler keeps appearing as a 'centrist' on r/PCM? - no he didn't roll over to the centre in his grave. Its revisionist and it was always meant to be. Let's never pretend the PC isn't pure revisionism.