This phrase comes from the Chinese Three Kingdoms period. According to historian Kenneth Hammond, during this time period, the model of the Chinese hero changed from one who wins by brute force to one who wins through cunning and strategy. The paradigm of this was the general Zhuge Liang.
In one of the great stories about him, Zhuge Liang’s army had exhausted their supply of arrows as they lay seige to a city. That evening, as a heavy fog rolled in, he sent boats out into the river manned by straw dummies. His enemies took the bait and fired on the straw “attackers.” Zhuge Liang’s army pulled the boats back in and used the arrows riddling the dummies to replenish their supplies. This story serves as the archetype of the general’s strategy.
The saying “straw boats borrow arrows” has become used in Chinese to signify that sometimes you can use someone’s one strengths against him.