If every proper subgroup of a nonabelian group is abelian, why must the group be generated by two elements?

Question

In my group theory class our teacher gave us this statement but I don't understand exactly why it's true.

Let $G$ be a non-abelian group such that every proper subgroup of $G$ is abelian, we can find $a$, $b\in G$ that satisfy: $$G=\langle a,b \rangle$$

Answer 1

Since $G$ is nonabelian you can find two elements $a$ and $b$ that don't commute. They generate some subgroup that's not abelian. If all the proper subgroups are abelian then that one must be the whole group.