Why is the moon white ??

Because your eyes aren’t that great at brightness.

As many people have mentioned, the Moon is actually quite dark grey:

However, it sure looks white to me. So what gives?

OK, look at this picture. Which square is darker, A or B? They’re the same color! Don’t believe me:

https://upload.wikimedia.org/wik...

It turns out we determine brightness in a very relative way. Square A looks dark because it’s surrounded by lightness. Square B looks light because it’s surrounded by darkness.

Sound familiar?

The moon is quite dark, but it’s significantly brighter than the night sky. As a result, your brain assumes it’s actually quite bright, when really it’s not.

You can really see this during a lunar eclipse:

See how white the right side looks? See how dark (and red…that’s from the Earth’s atmosphere…you can ignore that) the left side looks?

Relative illumination makes a huge difference in our perception of color and brightness.