The argument is when there are more than 2 options a majority of people would not have selected the “winner” over any of the other individual losers. Therefore majority rule is an illusion, democracy is self-contradictory!!!

However, by reducing the options to just 2 you no longer have the same result and “democracy” is more “self-consistent”. You can do this in a fair/Democratic way by “simulating” the pairwise interactions (IE ranked choice voting, pairwise majority rule, etc.) or by establishing a false dichotomy (2 party systems, left v right spectrum, etc.).

This is not ‘not a thing’ but it’s a really old idea and is largely solved (ie. Distributed networks like the social media platform we are currently on, or stuff like this).

However, the claim isn’t entirely misplaced as modern social institutions refuse to implement any of those methods because it would be against their best interests as those in power are deeply unpopular (yes, especially your favourites whoever that may be). So yes almost all “Democratic” systems you interact with on a daily basis are inherently self-contradictory on the most cursory of examinations, but they dont have to be.