The Mercator projection, designed in 1569 for nautical navigation and, for example, makes Greenland look the size of Africa. Greenland is roughly the size of Algeria (which is in Africa). Teaching it as the default map of the world gives every child (and some US Presidents) a fundamentally distorted understanding of geography, relative country sizes, and by extension, geopolitics.
The Peters projection or the Winkel-Tripel projection are more accurate representations of the Earth's surface. Neither is perfect (no flat map of a sphere can be), but both are dramatically more honest about the relative size of continents and countries.
Schools should teach the tool that reflects reality, not the one that was convenient for 16th-century sailors.