Meta-philosophy: What is philosophy?

So the semester is begining and in most of my classes I start off with the standard question of "What is philosophy?"  My standard answer is "The discipline that studies and examines assumptions."  This is a pretty wide net, but it has to be, since philosophy is a very wide discpline.  It does the job of including everything that is philosophy, and excludes everything that isn't.

But inevitably people still mistake philosophy with other things.  Religion is philosophy.  Poetry is philosophy.  Novels are philosophy.  So why aren't these things philosophy?

The most accurate answer would be that some of these things are philosophy, sometimes.  Religion, poetry, novels, etc are philosophy when they question the fundamental assumptions that we make.  But questioning is only the first step in philosophy, otherwise everyone would be a philosopher.  If everyone is a philosopher, then that means everyone does philosophy.  But I'm pretty sure everyone doesn't do philosophy, or at the very least, everyone doesn't do good philosophy.

Science begins with a hypothesis, but making up hypotheses doesn't make someone a scientist.  So what comes after questioning?  An attempt to answer the questions that we've raised using good reasoning.  This is the philosophical equivalent of experimentation. 

Now I get friends telling me all the time that my definition of philosophy is too narrow, or elitist.  Only good reasoning = philosophy.  But I think its reasonable to make a distinction between good reasoning and correct conclusions.  People can have good reasoning and be lead to incorrect conclusions.... I think.  And even if not, I think we can make a distinction of the quality of reasoning that philosophers engage in, versus non-philosophers.  Non-philosophers usually crutch on relativism or subjectivism to attack arguments.  Philosophers will usually look past such strategies. 

But I'm open to finding a better definition of philosophy....  I have a nagging feeling that my definition of philosophy casts its net too wide, including things that shouldn't be philosophy.