Hi,
hunting with a bow in Germany is illegal because someone added the ban when the hunting law was changed in the 1970s (actually without sufficient scientific research, as far as I know). Back then the bow technology was not as good and efficient as it is today. Efforts are underway to allow bowhunting in Germany again, but that will probably take a while, if it ever comes to that. Until then, German bow hunters have to hunt abroad.
Animal welfare also played a major role, which is very important in Germany (even more today than in the past). You are also not allowed to hunt with handguns or a crossbow. For the hunt for larger game (roe deer, mouflon sheep, chamois, wild boar, fallow deer, red deer) certain projectile energies at 100 m (1000 and 2000 J) and caliber diameter (6.5 mm and 2000 J for all game from mouflon and up) are required that they are legal.
Many hunters (and non-hunters alike) say that killing an animal with an arrow is cruel when it can be done much more efficiently with a bullet. And as long as there are such voices (including among the hunters), and there are many of them because they have no idea about bowhunting (and they don't care), it is very difficult to change anything.