Why does the Moon seem to follow us?
Short answer
The Moon is so far away that walking changes its viewing direction very little, while nearby scenery appears to move a lot.
How it works
Nearby trees and buildings shift greatly when the observer moves. Distant objects have little apparent parallax, so they seem to stay in place.
Key point
The practical point is this: Distant objects have little apparent parallax, so they seem to stay in place.