Why is it we should have to teach the history and philosophy of science.

History - to appreciate man's progress in understanding how the natural world operates.

Philosophy? Not sure about that, but it is important that all learn and understand the scientific method, so that the public can evaluate between various claims of scientific hypotheses. Every day there are news items in areas such as health, biology, global warming, and evolution (to name a few) - one should have a basic understanding of the science behind these issues in order to discuss them intelligently.

Philosophy-because for over 15 centuries philosophy was the way humans understood the natural world not through experiment like today but through reason so by philosophy it means how scientists reasoned and understood their world.
Hope this helps:)