This is a very idealistic and philosophical way to look at science, I know, but I'm an idealistic person. I try to teach what science should be, and so I will attempt to differentiate, where possible, between the ideal and the reality of a student as I remember it. What we're left with is the reality to deal with. In that sense, science is still very important since it is a natural product of an unrepressed curiosity. Science is also the source of new technology, whether or not society is ready to deal with it, so it can be frightening in this sense as well.
Science still is a logical process deep down, but it is very subtle.
It requires an insight that can only come indirectly, a fact that is a source of most of the frustration, I feel. Despite this, most people would be inclined to give science a 2nd or 3rd chance because of humankind's innate curiosity. Science is, in a sense, our future. That's because it tells us about our place in the world, and the directions science goes often define the direction society goes. So it is important as a bedrock in my mind.