I'm not sure what the word "teach" means, or whether it really exists. Semantically, it should be possible for a teacher to say, "I taught the pupils, but they didn't learn!" But does it make sense? And if it doesn't, why is there such a word?
In Hebrew, you don't teach. You can cause learning, you can assist learning, or you can learn with someone. They are all forms of the same verb—which happens to also be the 12th letter of the alefbet.
And it's the tallest one, too. Because that's what learning is all about: Reaching up to grasp something way beyond where you stand now. As for teaching--I mean, learning with someone--you also do the same: You reach down to touch someone who stands in another world from your own. And to do that, you need to reach very deep, to discover a point that transcends all those boundaries of you, other, his place, your place, worlds and reaching.
That's another reason why teaching is really learning: To bring someone else to learn, you must be learning yourself. And your learning must far exceed the learning of the other. Here's how it happens:
First, you learn something. You ponder and examine it for many years. Like, say, how to teach--I mean, learn. Eventually, you have your whole, unique world worked out, in which all of these thoughts fit somehow in place--never perfectly, always growing, but somewhat consistent nonetheless.
Then one day, you find yourself in the lab with a bright five year old granddaughter, and she asks, "How do you learn Kabbalah?"
You look at this little girl, and her mind is in an entirely different world than yours. You want to give her all the answer--not just a brush off. But to do that, you need to put aside your lexicon, your imagery, your set of metaphors--all the ways you understand this concept, and find some way to give her the essential concept that you have for yourself.
Which means, first and foremost, discovering what that essential idea is. That's the process called tzimtzum (we talked about it in the bagel, remember?) All the light of your understanding is put aside, leaving just that essential idea.
Next, you need to find a place in your own mind where you can imagine the mind of this little girl. And then you start slowly building bridges--parables, analogies, imagery and tight little explanations--until you connect that essential point with that whole new world it needs to enter. And then you can say it, and help it enter. (Or make an animation out of it.)
Now look what you gained: Before, you understood it in your own abstract world. Now you understand it in the concrete world of a small child, as well. Before, you understood the explanations and information. Now you grasp the central point--a point so essential, it can enter an entirely different world and remain the same nonetheless.
And another thing you learned: You can now have some inkling of what it means to create a world. For what you just did, that's essentially what the Boundless-Isifier-of-All-That-Is does to generate entire worlds out of absolute nothing: He imagines up worlds and then brings them into being by connecting them to His Infinite Light with a single, essential point, a point that can never be grasped or known, and yet through which all is known.
A.k.a., the Yud. As it says, "You made all of them with Wisdom!"