Some will say it does not matter, but at times it does. With standard straighter handled longbow grips, with some shooters, the arrow runs right on or barely missing the index finger. I shot right wing for years from my heavy right hand longbows. I had two bows that my finger was attacked frequently by the passing fletching. There are things that one can do with these to minimize it, but the easiest is just to go with left wing for right handed bows. For most recurves and hybrids it will make no difference which way the feather flies. With left wing on right hand longbows for wood arrows I fletch so that the feathers are an 1/8th turn rotated, so the bottom feather is not vertical as well.