No, the reasoning you presented is incorrect. The Earth is not flat but is, in fact, a globe. The idea that the Earth is a sphere has been extensively supported by scientific evidence and observations from various fields, including astronomy, geodesy, and satellite imagery.
When it comes to creating a two-dimensional map of the Earth, it is indeed impossible to accurately represent all aspects of the Earth's curved surface without some form of distortion. This is known as the map projection problem. Different map projections are used to represent the three-dimensional Earth on a two-dimensional surface, and each projection has its own strengths and weaknesses.
All map projections involve some degree of distortion, whether it's in preserving area, shape, distance, or direction. For example, a Mercator projection, commonly used in navigation, preserves shapes and angles accurately but distorts sizes and areas, making landmasses near the poles appear disproportionately larger.
On a flat Earth model, there are no scientific foundations to explain the distortion of distances or areas between cities because the flat Earth model is not supported by evidence. The overwhelming scientific consensus, supported by centuries of research and observation, is that the Earth is a nearly spherical shape, slightly flattened at the poles, and not a flat surface.
It's important to rely on scientific evidence, empirical observations, and expert consensus when considering the shape of the Earth, rather than entertaining unsupported and debunked ideas like a flat Earth.