At any given time, there is an equal area of the Earth that is experiencing daytime, and that is having a night time. The reason is that the sun is very far, and it would illuminate a hemisphere of the Earth, and leave the other dark.
If we plot which areas of the Earth that are getting sunlight on an azimuthal equidistant map centered on the north pole, the sun would appear to illuminate a somewhat elliptical area during the northern hemisphere summer, and a lopsided Bat-Signal shaped area during the winter. During the equinox, the sun would appear to illuminate a half-circle area.
This fact is not a problem because the azimuthal-equidistant is a map, and like any other map, it has distortions. An area of the map closer to the center represents a larger real-world area compared to the same map area farther from the center.
On the other hand, flat-Earthers insist the azimuthal-equidistant map is the map of a flat-Earth, devoid of any distortions. And this is a problem for them. They would have to invent just another ad-hoc ‘explanations’ how the sun illuminates such an impossible area. Their ‘lamp-shade’ or the ‘spotlight’ explanations fail to explain it.