Why study philosophy?

I won't answer the question myself, but just point you to this paragraph publicizing a day of talks and workshops at the University of Manchester for students from schools and colleges:

What makes our actions right or wrong? Is it OK to torture one innocent person in order to save the lives of a thousand others? Does God exist? How can we know anything about the world around us? Is my mind just my brain? Should we trust doctors more than homeopaths? What is truth? Is democracy better than dictatorship? Is it rational to fear death? What is time? If you find these kinds of questions interesting, then come along to Why Study Philosophy? and find out more!... You can come to philosophy with any academic background: you just need curiosity and an open mind. Philosophy asks - and tries to answer - the kinds of deep and puzzling questions that other subjects don't answer. So if you're interested in truth, beauty, right and wrong, justice, the nature of science, how language works, the meaning and value of life, the existence of God, the difference between rational and irrational beliefs... then philosophy is for you.

I might have added something about doubt, and about clarifying questions you're not sure how to answer, but there's enough there to be getting on with.