Orwell's better judgement tells him not to kill the elephant. Why, then, do you think he decides to kill it after all?
The Policeman feels compelled to shoot the elephant because that is what the crowd expects him to do. Even though he prefers to let the animal, now calm, live, he realizes that the demands of the crowd must be met. This has to do with the authority of the Police official in the colonized Burmese nation.
The Police official, the narrator, Orwell, understands the relationship that exists with the resentful colonists and the imperial force, the British Empire.
"As a colonial official, the narrator must not let himself become a spectacle before the native crowds. Not shooting the elephant would make him seem like a coward, so he shoots the elephant."
In order to keep order, and not allow chaos and a riot to erupt, the Policeman must shoot the elephant to keep peace in the town.