Why do map makers have to choose between showing the correct land shapes or distances on earth?

Map makers face a fundamental challenge due to the Earth's three-dimensional shape, which is a sphere, while maps are typically two-dimensional representations. This discrepancy necessitates the use of various projection methods, each of which prioritizes either accurate land shapes (conformal projections) or accurate distances (equidistant projections). As a result, an accurate portrayal of one aspect often distorts the other, compelling cartographers to make trade-offs based on the map's intended use.