Map projection is a way of drawing a sphere onto a flat surface. There's no way of doing this without introducing errror.
A "no error" solution of mapping Earth is the globe. But that is a sphere, not a 2D object.
So all 2D projections are inherently flawed. Richard Gott and Dave Goldberg identified 6 critical error types:
local shapes,
areas,
distances,
flexion (bending),
skewness (lopsidedness),
boundary cuts.
The most widely used one, Mercator projection, is great at preserving local shapes (handy if you're sailing the seas) but terrible at depicting areas far from the equator.
A new, 2D globe-like solution is the Double-sided disk map.