Why.doesn't the moon look full?

I had a sudden panic today. The moon was way up in the sky, in the middle of the day, i.e. at the same time as the sun was also way up in the sky. So, I thought, wait. there's nothing in the way of the sun shining on the moon, so why doesn't the moon appear full?

Well, of course, I'm not the only one to wonder that. And, once it is explained, the answer is obvious.

Yes, the sun is high in the sky, but it is off to one side as we look at it from earth. The sun is therefore shining on one side of the moon as we look at it, and so only part of it reflects back to us here on earth. It would only appear full to us if the sun was shining on it straight on (from our perspective).

Phew! Thank god there's a reasonable explanation.