Too far away to fall behind
Why Does the Moon Follow the Car?
The Moon seems to follow you because it is so distant that your movement cannot change its direction.
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Step 1 of 5
Nearby things rush past the window.
A hedge a few metres away changes direction enormously as you drive, sweeping from ahead of you to behind you within a second or two.
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Step 2 of 5
Distant things change direction far less.
A hill on the horizon shifts only slowly, because travelling a hundred metres is a tiny fraction of the distance between you and it.
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Step 3 of 5
The Moon is almost 400,000 km away.
Driving a mile is nothing against that distance, so the angle you look up at barely changes by any amount you could ever notice.
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Step 4 of 5
Your brain reads unchanging direction as following.
Everything else slides backwards while the Moon holds its place, and the only familiar explanation for that is something keeping pace with you.
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Step 5 of 5
The Sun and distant stars do it too.
This is not special to the Moon. The Sun, the planets and every star behave exactly the same way on a journey, for exactly the same reason.
You would need to travel thousands of kilometres sideways to shift the Moon's apparent position by a noticeable amount.
The short version
The Moon appears to follow you because it is so distant that no journey you make can meaningfully change the direction you look to see it.
Try it yourself
Cover one eye and line your thumb up with a distant building, then step sideways. Your thumb moves; the building barely does.
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