Can't a noun in plural form be described with a noun in singular form? of course it can. here are some examples:

> These workers make a lot of mistakes when they work since they are
> new to this job. **they are not the main reason we are losing money**, the state of the market is.

and:
> These people are my family

and also:
> We are a team!

If the above sentences sound grammatically correct to you, there's no reason why your teacher's sentence would be any different.
the quote you provided is perfectly fine and makes the same sense:

> These (things you need to do) are not (the) homework (you are
> obligated to do)