if you make a big balloon, paint it light green and the put it away, then put a progector on a distanse.

you will see that the sphere do not reflects the light the same amount at its all surface.

the moon give us the feeling that it is the same amount of light everywhere.

sould be darker while it goes to rounded surfaces from us.

The mathematical explanation: The density of reflected light passing through a 2D projection of the full moon is roughly proportional to the density of incident light. Since the density of incident light is equal across the entire projection, the density of the reflected light is also roughly equal.

I think it's like, your thing, or whatever, to completely flim-flam an explanation to fit your agenda. You just hope the person you're talking to is scared off by your use of unfamiliar terms and hypothetical mathematics enough to not question it. Not sure whether or not this is the case here, but I'm noticing a pattern.

I try to explain stuff in the simplest terms I can. I realize that my wording is rather confusing in this case, but I honestly don't know of a simpler way to explain it. Sorry.

Edit: Perhaps I can clarify some terminology:

Reflected light: The light that is going from the moon to your eyes.

Incident light: The light that is going from the sun to the moon.

"passing through a 2D projection": passing through a 2D plane in front of the moon

proportional: It increases/decreases by a constant ratio.

density of light: A loosely defined term. A more precise term would be radiant flux. I used "density" because it is easier to understand for the layman.

The technical term for the phenomenon I am trying to describe is

Lambertian reflectance. Read more about it at that link if you think I am just talking out my butt.