The moon does not reflect the light of the sun. How could such an obvious falsehood be cemented into our science and educational institutions?

There's a really simple test to see if the Moon is being lit by the sun when it is visible during the day: On a sunny day when you can see both sun and the moon, get a small ball and hold it at arm’s length so it lines up with and covers the moon. If the moon is being lit by the Sun, and the sun’s rays are roughly parallel between you and the Moon, the same amount of your ball will be sunlit as the lit portion of the moon - e.g. if it's first quarter the ball will show a quarter, if it's half the ball will be lit by half, full the ball will be fully lit and so on.

I’ve done that test many, many times - the ball and the moon always match damn near perfectly. And it always does give the same result - the lit portion of the moon matches the lit portion of a ball held up in line with the moon. Absolutely don’t take my word, go and try it. To illustrate what I mean here are some pictures I took of the test - though to be ‘proof’ you should really try it yourself, as this is the era of universal photoshop !