For most people who are not navigators, and for most purposes, area matters more than angles. Land area matters more than sea area, and largely uninhabited area does not matter much.
There is no "mathematically correct" projection.
Go to the equator. Move about 10000 km in a straight line along the equator. Turn 90 degrees and move about 10000 km in a straight line to the pole. Turn about 90 degrees and move about 10000 km in a straight line to your starting point. Turn 90 degrees to get to your original facing. A triangle with a sum of angles of 270 degrees. On a flat map either the lines or the angles must be distorted, or both, because a flat triangle has a sum of angles of 180 degrees.
So which distortion do you use?
Depends on your purpose. You get a choice of where and how the surface of the sphere gets distorted.
- It is common to accept a distortion at the North and South Poles. That is really dangerous when one thinks about Cold War military strategy, and about why Russia might feel encircled right now.
- One could say that it is no problem if Canada, Greenland, and Iceland get inflated on the map. Snow, ice, more snow, few people.
- It could be a problem if Central Europe appears inflated. They've already got the Prime Meridian, and now that, too. That could lead to excessive notions of their importance, and ignoring the sheer size of the rest of the world, especially equatorial regions.
- Distorting the southern hemisphere is seen as less of a problem. Few people live in Antarctica. South America and South Africa are relatively small landmasses projecting into the ocean. For Australia, the Greenland argument holds -- miles and miles of miles and miles.
Look at this map, Alaska appears bigger than India ...