To quote H.L. Mencken (paraphrasing), a teacher's job is miserable because they must ceaselessly try to get masses or people to think who have no real capacity to.

You might be lucky to reach a small minority of your students, assuming environmental forces of poverty, dysfunctional family, and peer influence don't muzzle their gifts. But the day in day out bulk of your work isn't those "Mr. Holland's Opus" moments: it's handling a bunch of kids who don't want to be there in a bureaucratic set of rules imposed on you from above. And private schools are not immune to these problems either.