Next time you see the moon, cover it over with your thumb or index finger extended to arms length. The angular diameter of the moon (and sun, for that matter) are really tiny.

Your brain just imagines that you see it closer/bigger when looking at it, especially if it's near the horizon/through branches/other things on the ground. This effect gets more pronounced the longer you stare at it. I think this is why it's so hard to get a picture of the moon that looks like how you see it, unless you use an impractically long lens.