As a civil engineer friend of mine like to say, it's a lot harder to build things than tearing them down. A terrorist doesn't have to be as smart as we are because his mission is fundamentally one of destruction.

As an aside, there are some problems which can only be solved via violence. The Taliban comes to mind. After years of sanctions as well as diplomatic/economic pressure, it was 3 months worth of direct application of violence that brought the Taliban down.