The concept of bows and arrows, while not too complicated to develop, doesn't seem like a technological advancement so natural to grasp for virtually every group of humans on Earth to have developed at some point. Even the North Sentinelese people, reportedly the most willingly isolated society in the world, have developed it. Why and how is that?
As you can read in our FAQ on the topic, the bow and arrow has appeared at various points and places throughout history. Since every element of the contraption is perishable, it is difficult to track a definitive history of device, since its use extends several millenia back. A purely dispersionist model, with a single development, is not accepted. As for the "why and how" of its development, I'd recommend delarhi's answer here about "solution spaces": people faced with the same problem develop the same solution, because no matter where you go the solution still works.