The apple is an interesting fruit. [the entire class, general statement]
An apple a day is good for you. [refers to apple as a class, a fruit from the class of fruit known as apple]
Apples are good for you. [General statement with the plural]
Please note: in statements with an A, the same statement can often also be made by pluralizing the word.
That is what your professor meant.
That said, the word people is irregular. It is not a regular countable noun and has specific rules. Because it has two basic meanings and can be used in different contexts.
If one says: a people, it means an ethnic or national group. It does not mean: The people you see in the street.
For example: The Hittites were a great people. The Ameridians of North American were once a proud people
Compare: The Hittites were great people. (Impossible to verify but that means they were nice people!)
Also, in everyday usage, the word people can take nothing: People in England drink tea. In that sense, it is for a general statement, and the word does not take a or the.
Also, for example, The people in the street are moving fast. Why /the/? It would imply you are talking about only those ones and not The people in the building. In that sense, it is specific. Here, the /the/ does not refer to the entire class of people. It refers only to the specific ones (in the street versus in the building).
General statements about people in the everyday meaning: no article.
General statements about specific people, everyday meaning: the, the people in the room (versus those outside it.), the people in this forum
General statements about people who "belong" to a particular place: the, The people of France are fed up with the situation. The /the/ is there because of genitive (of France, the ones who belong to France). Another example: The people of Athens were not all Athenians. Same idea.
That pretty much covers people except for the plural as in:
The peoples of Europe have done some awful things to each other down through the ages. It is often seen in the Bible, too.