Probably because the relative speeds are so fast, that if they launched it even seconds later they'd need to plot a whole new course. The comet is moving at a relative speed of something like 23,000 mph.
There maybe a trajectory that uses the gravity of another planetary object to achieve the necessary speed.
Makes sense. Seems impossibly small though. I would think that even the slightest ability to tweak the trajectory early in the flight would make the launch window a bit easier to work with.