I was wondering that too?

lære can mean both learn and teach, while undervise can only mean teach.

Let's look at the two in the meaning of to teach:

at lære [NOGEN] [NOGET]

Jeg lærer børnene hvordan man binder snørrebånd

I teach the kids how to tie their laces

Here, but the direct object and the indirect object are required.

at undervise [NOGEN] [i NOGET]

Læreren underviser eleverne i samfundsfag.

Here, you can leave out the direct object ([i NOGET]): Jeg underviser gamle mennesker.