The Earth is a sphere, a three-dimensional shape. But most of the time, we work with two-dimensional media, including paper, computer displays, televisions, phone screens, whiteboards, etc. To represent the Earth on a two-dimensional medium, it is necessary to transform the curved shape of the Earth’s surface into a planar form using one of the many map projections.
All map projections necessarily introduce distortion into the results. Some flat-Earthers think that distortions are ‘evidence’ of failure of modern science to explain the world. They are wrong.
Map distortion is merely a consequence of converting a three-dimensional curved surface into a planar form. It is impossible to create a map without distorting it in some fashion, the same way it is impossible to perfectly flatten a ball without cutting it.
Some of the resulting distortions are acceptable, and others are not. Many different map projections are created to preserve different properties of the sphere-like body at the expense of other properties. Therefore, a projection can be suitable for a purpose but not for others.
The so-called ‘flat-Earth map’ is claimed to be distortion-free, and some flat-Earthers take that as proof of its correctness. They are wrong. A map can only be distortion-free if the actual shape it represents is also flat. But this is not the case.
All maps of the Earth have distortions simply because it is a two-dimensional representation of a three-dimensional object. It doesn’t mean a distortion-free representation of the real Earth does not exist: we call it a globe.