So the question has been asked, "why didn't the land of the samurai warrior man up and shoot down those North Korean missiles as they flew over the Emperor's sovereign territory?". Well, taking a step back, at least this time Japan saw the missiles coming as opposed to the first time back in 1998 when Kim - "the middle one", lobbed a patriotic singing grenade over the country and the government had to be notified via a small telephone from America (though the same is true of the Russians who also missed it in flight, though apparently, as was later explained, it had been tricky and swerved to avoid their sensors).
But before we arrive at an answer, there is the slight confusion as to whether Japan already is actually currently able to shoot down a ballistic missile aimed in its general direction (Monty Python spoiler alert) or does the country need to purchase yet more kinetic hardware from the shelves of Lockheed Martin Space Systems to resolve the issue once and for all? A ponderance that begs the question "what exactly are those Patriot Missiles doing lying around the Ministry of Defense in downtown Ichigaya if not to defend against in-coming?" But let's save that for another day.
So could the reasons that Japan decided not to press the button really be two fold. Firstly, if something is flying towards you, shooting it down enhances your chances of cranial injury; i.e. if you shoot at a duck, it might just spear you out of a refined sense of irony. Point made; the second main, and much under-reported, reason for not shooting at these ballistic javelins was that as they traversed Japan, they were at a peak trajectory of some 750 miles. That's roughly double the altitude of the International Space Station to put things in perspective. Japan knew these missiles were going going to miss by the proverbial mile. And as legend would have it, those wily samurai also knew both when, and importantly when not, to shoot at a duck.