Why does Katniss kill Coin?

After Snow is tried and found guilty, he told Katniss that the final assault that killed Prim was ordered by President Coin, not the Capitol. Katniss realizes that if this is true, the bombing that killed  Prim, may have been the result of a plan originally developed by her friend Gale. Katniss realizes that she will never be able to look at Gale the same way, regardless of whether he was directly involved in Prim's death. Katniss remembers a conversation with Snow in which they promised not to lie to each other. When she is supposed to execute Snow, she realizes that he was telling the truth and kills Coin instead. A riot ensues and Snow is found mysteriously dead, having possibly choked on his own blood or trampled in the crowd.