The scientific method is based on what I prefer to call the inquiring mindset. It includes all areas of human thoughtful activity that categorically eschew "belief", the enemy of rationality. This mindset is a nebulous mixture of doubt, questioning, observation, experiment and, above all, curiosity, which small children possess in spades. I would argue that it is the most important, intrinsically human quality we possess, and it is responsible for the creation of the modern, enlightened portion of the world that some of us are fortunate to inhabit.
Curiously, for the majority of our youth, the educational system magically causes this capacity to disappear by adolescence. Without it, we have no instinctive ability to assess the importance of the technical issues that impinge on our everyday lives. We are unable to gauge accurately the validity of fears over such issues as climate change and the looming energy crisis, or grasp the socio-economic and humanitarian importance of new genetic technologies.
Scientific education is by far the best training for all walks of life, because it teaches us how to assess situations critically and react accordingly. It gives us an understanding based on reverence for life-enhancing technologies as well as for life itself. If we do not know how things work, how can we fix things? And how are we going to use these powerful technologies wisely?
I've always argued that more than the material itself, the ability to analytically think things through, and to analyze the validity of a result/conclusion, are more important, especially for people who are not going to be scientists and engineers. Such skill is severely lacking in many people, because they seldom look behind the statements being made, often by politicians and talking heads on TV.