Here's why:
* Common nouns refer to general categories of people, places, or things. They are not specific to any one person, place, or thing.
* Proper nouns are specific names of people, places, or things. They are always capitalized.
For example:
* Common Noun: teacher, city, river
* Proper Noun: Ms. Jones, Paris, Nile River
Since "dance teacher" refers to a general category of people who teach dance, it's a common noun.