The Mercator projection is not a mistake at all, it just chooses trade-offs when mapping a 3D sphere to a 2D plane that are relevant for marine navigation (preserving angles and directions, but not sizes for example). So if you want to do marine navigation, it's a good choice (no mistake). I can imagine it's not the best choice for things like Google Maps and learning maps in school, so the choice for Mercator could be considered a mistake maybe.

I didn't meant it is a mistake as a projection but as a choice adopted for everywhere you look.

Meractor is no more of a “false map” than any other projection.