Teaching, we learn.
As it stands, a maxim, and true as far as it goes. But in need of qualification which, when added, makes it a maxim no longer. Brevity is essential to the maxim as it is to the aphorism and the epigram.
Closer to the truth is the following. Teaching, we learn; but only up to a point beyond which studying without having to teach is much to be preferred if the goal is an advance in understanding and erudition.
I never knew logic so well as after having taught it for a couple of years. But then the maxim lost its truth.