Learning = admitting you're not as clever as the others?

How come as soon as something becomes too difficult to solve, all math teachers say "I'm not gonna bother doing this, cause I can't think of a simpler way of solving it, except if you have a list of integrals like this one in your notes to look at" (Hello..? We're not allowed to have those on the exam anyway, now, are we? Didn't think so). How come they only ever solve simple examples, and when it gets to the level we're supposed to be on, they can't be bothered to explain how to? It doesn't seem to matter if you're at KTH, MIT, or anywhere else, cause this is the exact scenario:

1) They say "You'll just have to trust me that this is the correct answer."

2) All the students laugh.

3a) A select few know how to solve it.

3b) Some go home and solve it on their own. If they don't get it, they'll ask the teacher for help.

3c) The majority goes home thinking they're gonna work it out by themselves and ask the teacher before the next lecture if they still don't get it. They end up not doing it, and they're toast when it comes to the exam. (Guess in which end of this I've been living for the past two years. And before that I rarely had to ask anything - I was one of those a) category people who just got it anyway.).

Maybe we should all become math teachers? Anyone can understand the basics and learn how to write on a board. If a student then needs help with a really difficult problem, you can always tell them to ask a course assistant instead of you. And there will always be the ones who are too uncomfortable to ask in the first place. Admitting to not knowing something you know you should know is embarassing. But not asking is stupid. Maybe that's what learning is all about - being able to humiliate yourself for the sake of understanding, and remembering that most people actually can't learn something properly without asking.

Yeah, I'm slightly bitter. Angry with myself. Embarassed. None of which is any teacher's fault, really. Cause it's my responsibility, no matter who the teacher is. He or she could be awesome or rubbish, it's still up to me.