One often hears that philosophy deals with "why" questions, whereas science deals with "how."  Some philosophers will say that science can never answer why we exist or why the universe came into being.          
        But "why" questions are often in reality "how" questions.  Futhermore, not all "why" questions are meaningful in that they presuppose "purpose" that may not exist.  It is meaningless to pick up a rock and ask, "why is this rock?".   Most "why" questions can be broken down into "how" questions, e.g. "How is a rock structured?"  Oxford Professor of Chemistry, Peter Atkins has said on more than one occasion that theologians and philosophers have over millennia generated a number of false "why" questions. For example, "why does the universe exist?"  In other words, "what is the purpose of the universe?"  The answer of course is that the universe has no purpose.  Purpose is only meaningful when dealing with intentional agents.  We can not apply the intentional stance to the universe.
        But what of the real questions?  How has the present universe emerged?  I would agree with Professor Richard Dawkins that if science is unable to answer a real question, philosophy certainly cannot.  But I would like to add that science is a branch of "natural" philosophy.  Science is the branch of philosophy that emerged in the course of history as the only consistently reliable means we have of acquiring knowledge, thus we may relegate "classical" philosophy to historical studies, whilst keeping logic, discussion, argumentation and the scientific method in our toolkit.   
        We owe philosophy a debt, for it has given us logic and led us eventually to the scientific method.  Natural philosophy combined logic with knowledge of the natural world, and then once we applied empirical method, we arrived at science.  So, now that we have science, is there a place for the teaching of philosophy?  I think there is a place for the teaching of logic, discussion, argumentation, and of course epistemology, i.e. what is knowledge and how do we come by it?
What exactly is the difference between philosophy and science? For example, a philosopher who teaches logic along with the importance of empirical data for testing the soundness of logical premises can be seen as a scientist who does not actively engage in experimental research, and conversely, a scientist is in a sense a naturalistic philosopher who performs experiments.  But experimentation, the testing of speculation, is crucial. Speculation alone can never prove how things are in reality. Knowledge is by acquaintance. We must go out, look at the world, and test our ideas.
        Are there questions that can only be answered by philosophy?  For example, can philosophy alone answer or attempt to answer the question of what one ought to do?  There is no reason to suppose this is the case.  First we must examine what is meant by "ought."  If "ought" refers to an absolute, inalterable standard of right and wrong, on careful inspection it is evident that no such thing exists.  Similarly, the idea of a human-independent, timeless, cosmic moral standard does not bear scrutiny.  But if by "ought" we refer to what is necessary for individuals to coexist in the world without destroying one another, and if we recognize that there are clear advantages to working in collaboration, then we may appeal to reason.  Treating others as we would have ourselves treated, and not treating others as we would not have ourselves treated is reasonable.  It is a rational strategy for survival and happiness.  
        "But all who are not lunatics are agreed about certain things: That it is better to be alive than dead, better to be adequately fed than starved, better to be free than to be a slave. Many people desire these things only for themselves and their friends; they are quite content that their enemies should suffer. These people can be refuted by science: Mankind has become so much one family that we cannot insure our own prosperity except by insuring that of everyone else. If you wish to be happy yourself, you must resign yourself to seeing others also happy."  (Bertrand Russell)  
        Any society in which citizens regularly rape, maim, and kill one another with carefree abandon will soon disappear.  Both philosophy and science can provide answers as to how we "ought" rationally to behave in the interests of survival and happiness.  Philosophers observe the human condition, apply logic, engage in discussion, etc.  But then scientists also make observations, apply logic, and discuss problems with their peers.  Most importantly, they test their hypotheses against data.  
        Science may also shed light on empathy and altruism in our species.  Human minds have emerged under the pressures of natural selection over hundreds of millennia; our sense of right and wrong may be described in terms of the complex interplay of our inherited equipment and the environment in which we live.  
        Again, there is no absolute, inalterable moral code, and no evidence of a cosmic arbiter either.  But science can help us decide on how individuals and societies ought to behave to achieve the maximum flourishing of our species whilst minimizing suffering.
        Science is not less capable of answering real questions than armchair philosophy.  If anything, science encompasses philosophy, whilst adding to it the power of the scientific method.  In this way, science is arguably the pinnacle of the philosophical endeavor.  It is our most effective epistemological tool.
        Let me add however that I do think philosophy has an important role to play in education.  I think there is a false but popular impression that there is a clear demarcation line between science and philosophy.  It might be better to think of it as a continuum.  Science has emerged from philosophy; it is a branch of philosophy.  Science and philosophy are not antithetical to each other.  On the contrary, the methods of philosophy, i.e. logic, discussion, and argumentation, are encompassed and added to in the form of science.        
        “Every science begins as philosophy and ends as art; it arises in hypothesis and flows into achievement.”  (Will Durant, American writer, historian, and philosopher)
        Historically, philosophy has often been our first attempt at understanding phenomena.   A branch of epistemology matures, and as more data come in and empirical method is applied with greater rigor, philosophy flowers into science.  Consider that psychology was once a metaphysical philosophy.  Now it is a science, at least insofar as it is commensurable with the scientific method.  Cognitive science in its earliest form began as pure speculation, and we have seen it approach a science as more is learned and as neuroscience lends greater ability to render hypotheses quantifiably discrete and testable.  There is no reason to suppose that this trend will not continue.  We may be optimistic that science will continue to make progress into areas that were once the provenance of pure speculation.