Why are all map projections not accurate

All map projections are inaccurate because of the shape of our world compared to the shape of our map. The shape of the world is a sphere (or a near sphere). Simplifying that to the second dimension, we still have that the world is a circle. But, maps are rectangles, so since there is a difference between a rectangle and a sphere, all maps will be inaccurate. But, many maps will be close, and will be bad in one area (such as size) but compensate in another (such as distances between continents and such). Something cool about map projections is their name (projection). They are called a projection because points on the globe are shined on with light and then the location they are on the map is where they are marked, meaning that they are 'projected' from globe to map.