There are several reasons why Song Jiang poisoned Li Kui.
First of all, from the perspective of the righteousness of the rivers and lakes, Song Jiang was out of concern for Li Kui and an in-depth understanding of his character. He knew that Li Kui was short-tempered and loyal to Song Jiang, and if he learned that Song Jiang's ** minister was killed, he would definitely rebel against the court and avenge Song Jiang. Song Jiang didn't want Li Kui to be in danger because of this, nor did he want his reputation to be ruined, so he decided to poison Li Kui and let him die with him.
Secondly, from the perspective of power and status, Song Jiang may also have taken into account Li Kui's status and influence among the heroes of Liangshan. Li Kui was an important figure among the heroes of Liangshan, and if he lived, he might become the leader of other heroes and continue to fight against the imperial court. And Song Jiang has accepted the court's recruitment and become the ** of the court, and he doesn't want the heroes of Liangshan to become the enemies of the court again. Therefore, he poisoned Li Kui in order to eliminate this potential threat.
In addition, from a psychological point of view, Song Jiang may also have jealousy and uneasiness towards Li Kui. Li Kui has a high prestige and influence among the heroes of Liangshan, while Song Jiang, although the leader of the heroes of Liangshan, may not be as good as Li Kui in some aspects. This jealousy and uneasiness may also have been one of the reasons that prompted Song Jiang to make the decision to poison Li Kui.
To sum up, the reason why Song Jiang poisoned Li Kui may be out of concern for Li Kui, an in-depth understanding of his character, consideration of power and status, and personal psychological factors. However, it is important to note that these reasons are not the absolute answers, because the psychology and behavior of characters in history are often complex and changeable. Moreover, the question itself carries a certain element of speculation and reasoning, as historical truths may never be fully revealed.