According to the laws of the Song Dynasty, there are three kinds of killings, namely, homicide, vendetta and fighting. Homicide and vendetta all belong to the crime of intentional injury, and they have to pay the price of their lives, but the third one is unnecessary. Fighting and killing people is killing people by mistake because of fighting. This crime requires no beheading, only exile.
Therefore, before killing Pan Jinlian, Song Wu stripped off Pan Jinlian's clothes, just to create a scene in which the two of them were fighting, and then killed Pan Jinlian by mistake, creating an illusion of fighting for the government. The government also killed Pan Jinlian and Ximen Qing by mistake because of Song Wu's fight, so it exempted Song Wu from the death penalty and exiled Song Wu.
Therefore, although Song Wu has a skill and martial arts, his heart is also very thin, not a man of five big and three thick. He was sober-minded when he took revenge, which could reduce the crime. If Song Wu directly killed Pan Jinlian at that time, even if the local government wanted to be partial to Song Wu, it could not be partial because there was no reason. Song Wu could let the government turn the case into a fight, thus saving Song Wu's life.