What’s your preferred projection?
To say that Mercator “lies” is to misrepresent the complications of projecting a 3 dimensional object onto a 2 dimensional surface. All projections “lie” in this sense because they’re simplifications of reality - that’s what a map is.
this video is based on the comic: it’s an animation on how each projection would change when shifted.
Mercator is the most accessible paper map. The Authagraph is the most accurate due to low distortion. It’s not listed in the comic, and can be confusing to use as a learning tool.
The real question is why are you so committed to flat maps in the digital age? I don’t even understand why Google Maps doesn’t correct to a spheroid when zoomed out like Apple Maps, requiring users to download Google Earth for accurate representation of land mass size comparison.