The original meaning came from Old and Middle English word, syn. Which means offense or misdeed. The meaning was corrupted by the Latin derivative, sōns when the Catholic church was in its heyday. Sōns means guilty. The old meaning referred to an act that may have harmed or caused distress to others thus making one culpable for errant actions. The Latin corruption was an ideological shift which incorporated the concept of Original Sin. Humanity's state of "sin" caused by the fall of Adam and his expulsion from the Garden of Eden. Thus spawned the practice of infant baptism. It was once believed that children (even newborns) if not baptized, were condemned to Hell. Later it was decided they ended up in Purgatory. Neither Heaven nor Hell. Responsibility for offense or misdeeds switched to the priests and the confessional. One was absolved with the help of a little ::cough::bribe::cough:: donation. This was one of the reasons the Reformation came about and 600 or so years (give or take a few hundred years) of sectarian violence and war.
Anyway, the origins of the word sin are a little more complicated than an archery term.