Why moon is not a proper noun?

The noun moon is a common noun because it is a Word for any kind of moon anywhere.

A proper noun is the name of a person, place, thing, or a title; for example:

• Moon Unit Zappa (real name), actress
• Moon Township, PA
• Blue Moon Cafe, Sedona, AZ
• 'Tell Me That You Love Me Junie Moon' (1970 movie), with Liza Minnelli

Moon can be both a common and a proper noun. There are several moons (common noun) in our Solar System, and we refer to The Earth's natural satellite as The Moon (proper noun.)