The December solstice occurs between the 20th and 22nd in December, which is when the Sun reaches its most southerly excursion. Around this time, the northern hemisphere experiences winter, and conversely, the southern hemisphere experiences summer.
If we try to plot the areas that are having daytime and nighttime on the so-called ‘flat-Earth map’, the Sun would appear to illuminate an impossible area, similar to Batman’s bat-signal. This fact tells us that the ‘flat-Earth map’ does not conform with reality.
On the ‘flat-Earth map’, the Sun would illuminate the ‘flat-Earth’ all the way to the edges, except for some parts in the middle which is having the night time, in shape not unlike a lopsided ‘bat-signal’. Furthermore, the Sun is at the farthest point from the opposite side of the Earth that is getting the sunlight all day.
To verify this, anyone can make sure if the Sun is still visible on the opposite cities in the illustration. Even if there are no big cities located south enough, we can still conclude it is impossible for sunlight to behave like this.