Earth v. Moon

The attached diagram shows how the angle between the moon and the observer's vertical varies at different times as the Earth rotates.

Photo credits:
Earth: Visible Earth, NASA.
Moon: Kopfjäger (Away) on flickr, CC BY 2.0

Think about it this way. Suppose you are standing on the Moon at the point nearest the Earth. Thus the Earth is directly overhead of you. You lay on your back to see it clearly. Now on your back you can rotate so the "half-Earth" appears in any direction you like. Right?

Now pick and orientation you want to view the Earth. As you lay on your back on the Moon I walk in the direction your head is pointing until I'm a quarter way round the moon. I'll be standing up but oriented exactly as you are laying down and I'll see the Earth's phase at the same random orientation you chose when you laid down.

It is a matter of relativity of orientation. Forget the moon is there and imagine you are floating in space. Pick the orientation you want to observe the Earth and then imagine the Moon appears below your feet.

BTW, I lost the bet with my friend. That sux!

Small price to pay for greater knowledge. (Or was it small? How much did you loose?)

What mechanism would make the illuminated portion of the Earth at the top, and the illuminated portion of the Moon at the bottom.