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

Maps are flat and the Earth isn't. This is based on the reports from explorers who had sailed the oceans, geographers realized the Earth was not flat. Then a new model of the Earth had to be found. After a globe, a spherical scale model of the planet was invented. The globe of the Earth best shows the sizes of continents where mapmakers have to choose between showing the correct land shape or distances on earth.