Here's why:
* Common nouns refer to general things, places, or people. They are not specific to a particular individual, location, or thing.
* Proper nouns are specific names for people, places, or things and are always capitalized.
"Community pool" is a general term that could refer to any pool owned by a community. It's not a specific name.
If you were referring to a specific pool, like "The Oakwood Community Pool", then that would be a proper noun.