two boxes kept in contact with each other exert normal forces on each other....not considering it as system why dont they move apart

 if there is no external force on the blocks then he normal contact force between them is zero    and so they remain sationary 

To understand your question in simplest way , take both of your boxes to space , you will see there is only force between them for which they will move towards each other is gravitational force , Normal force is an electromagnetic force you can understand this like suppose there are N molecules bound on a surface due to inter molecular force so when you push one molecule obviously the intermolecular force which is electromagnetic in nature will try to bring that molecule back to its position. hence by pushing a molecule you yourself will also experience force which is electromagnetic . Now for the two surfaces of the box and How do you think you can bring this elecromagnetic forces in to picture ?? simply by pushing the molecules. And the problem gets quite intrestingly intricate when you have Zillions of molecule on one surfce of one box pushes the other zillions of the next box so the we can safely say that the contact  force you are talking about is essentially the vector sum of these tiny electromagnetic forces between the Zillions of molecules of both the surfaces of your BOX. You knoe the Intresting point is the vertical componet of this contact force is NORMAl force and the Horizontal component is the friction force !! I believe now you got an idea why they dont move ?? Let me know for further clarification.