Why is the moon in photography much bigger than what the naked eye sees?

This is the perspective compression effect of telephoto and ultra-telephoto lenses.

The principle of camera lens imaging is the same as that of the naked eye. Starting from the pupil (or the lens of the camera), the fan-shaped space seen from a certain angle is projected onto a rectangular (negative) or arc-shaped (retina of the eyeball) picture. Therefore, when the narrow close-up in this sector space is projected to the lower part of the screen, its area on the screen is the same as that of the wider foreground in the sector space at the upper part of the screen. This makes the distant scenery relatively smaller, which is called "perspective". The telephoto lens reduces the angle of the fan-shaped space, so that the distant scene in the photo will not be excessively reduced. It makes the scene at the top of the picture almost as big as the close-up in front of you, as if it were pulled closer to your eyes.