Flat maps distort the spherical Earth. By how much, exactly? This 1947 film draws a world map on a grapefruit and unpeels it in various ways to show how the land masses' sizes and shapes change when they get projected on a flat surface.
Even if you use a globe, you can't really see what the true size and shape of continents are because the parts of the globe farthest from your eyes look smaller than the part nearest your eye. To see the land masses as they are, you need to build a giant hollow globe that you can stand inside with your head at the center so that all points of the map (painted on the inside of the shell) are the same distance from your eye.