Swords are DEX weapons, bows are STR weapons, not the other way around.
Swords aren't heavy. Longswords are only about 1.5kg and even greatswords are only 2.5-3kg. They do not require much strength to wield, and you don't need much force behind a sharp sword to do serious damage. They are levers, you produce force through chain-of-the-body and proper structure. Reflexes, timing, distance, precision and speed, the ability to correctly read and respond to your opponent is what is necessary for swordsmanship.
The power behind an arrow is directly proportional to the strength required to draw the bow. They are strength weapons in all the ways swords aren't. Medieval archers trained since early childhood to be able to draw and fire heavy war bows. Dexterity is secondary to them, it doesn't matter how precise your aim is if you can't draw the bow properly.
I'm fucking tired of this idiotic stereotype.