This might not be the answer you’re looking for, but i am just proposing another version of what teaching is.
Just like parenting, you are not dictating the direction to which your kid is going. What you are doing is providing framework to any kind of possibility to where they CAN go.
When I was in senior high school, one of my friends asked our math teacher as to why we have to learn linear equation, quadratic equation, normal curve, etc yadda yadda blablabla. I still remember that moment clearly because I, too, did wonder about the reason.
Few days back, Mas Hafiz gave me an answer for that, as follows:
The free interpretation is more or less like this:
“Just like army, they have to do push up, heavy lifting, etc etc while their main job is defending the nation in the front line of a battle. Do you think upon meeting the enemy they should do those exercises they do in daily basis? Math is like that. It is an exercise for your mind so that in real life, being faced with problem that requires high performance of the brain, yours is ready.”
Another fella also said that in school, you are not necessarily supposed to learn things that answer the current affair, because the problem in real life is so much different than that in text book. Not to mention how limited time we have in school compared to myriad problem in real life. Not to mention by the time you are graduating, the problem will be much more different.
That much is true.
The problem human have to face is constantly changing and is almost impossible for the average human being to keep up with THROUGH school. So, when teaching, you are molding your students, providing framework in their intellectual mindset, show them the way to problem-solving instead of mere force-feeding them with information of the current affairs. You teach them self-discipline and constantly inspire them to aspire to be anything they want to be, and show them all possibilities in life.
That is another version of teaching definition.