Teaching children to think for themselves: subject choice in the secondary school

When I was teaching high school I worked in an extremely selective and highly academic environment.  I found there were two kinds of students in my highly 'subjective' humanities field of Music.

There were the ones who wanted be given appropriate tools and stimulated to explore their own capacity for thought, then draw their own conclusions about a question and work out a way to support their argument with facts. 

And then there were the ones who wanted you to give them the answer, so they could learn it off by heart and regurgitate it in the exam. Invariably, the latter students had parents who had decided that paying private school fees gave them a right to their children being spoon-fed the correct answers for everything, which would (in their minds) inevitably lead to the high-ranking pass in the final exams which they had paid for.

No prizes for guessing which learning strategy results in the more productive member of a workplace, not to mention the most likely citizen of Planet Earth to help us solve our very real problems.  The reluctance and inability of some people to work with joy and self-belief within a grey area is, I find, extremely worrying.

What is your feeling on this?  If you enrol your child in an expensive school, do you think you've purchased a pass mark at day one?  Do you value subjects with clear right-and-wrong answers, like  maths, above subjects which involve some degree of informed choice in the response?  Do you actively steer your teenager away from subject choices which involve original thought?

Or do you look at secondary schooling as an opportunity for your child to learn to think for themselves, in the hope that this will lead to success?