Like so much of what Brian endures, there seems to be an ongoing dialectic where he experiences something bad, following by something good, succeeded by something bad. The bow incident is no exception to this. His experience with the first bow spells near disaster for him, as it almost ends up wounding him. I would pay attention to Paulsen's description of this event in the middle of the book. Brian is able to understand how the bow was calibrated incorrectly and nearly hit him. He grasps this, makes the modification, and then is able to produce a bow that is able to hit the fool birds and generate both a new source of food production as well as protection device.
More than that, Brian's first attempt at making a bow for his arrows comes close to blinding him. He has made the bow "too stiff"; it snaps, sends pieces of wood into his face, an inch or so above his eyes (p 124-125). Brian is indeed able to see the incident as one of many in which he has learned valuable lessons, though. The first bow "looked beautiful"--but the looks were deceiving, almost costing Brian his sight. In that setting, that would be probably have been fatal.