How it is not a mistake?
Because as you see, old map is everywhere and is used for everything.
Just open Google Maps and see.
It's not fair to make a false map a standard being used for everything.
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.