The Burmese people were not permitted to own firearms. But when the narrator encountered the elephant, why did he not have one of the Burmese people accompanying him fire the rifle?

As a British police officer in Lower Burma, the narrator is expected to act resolute and authoritative at all times because he is an extension of the ruling imperialist regime that oppresses the native Burmese citizens. Despite the fact that the British officer has no intention of shooting the elephant and does not want to kill the tranquil animal, he understands that he must behave like a brave, callous authority figure in front of the natives. If the British officer were to offer his weapon to a native, he would appear weak and timid. The officer's dilemma highlights how imperial conquest also oppresses the agents of the ruling nation to act against their conscience in order to maintain a resolute, authoritative appearance. The British police officer elaborates on his dilemma by saying,

Here was I, the white man with his gun, standing in front of the unarmed native crowd—seemingly the leading actor of the piece; but in reality I was only an absurd puppet pushed to and fro by the will of those yellow faces behind. I perceived in this moment that when the white man turns tyrant it is his own freedom that he destroys. He becomes a sort of hollow, posing dummy, the conventionalized figure of a sahib (Orwell, 3).

Overall, the British police officer must shoot the elephant because of the immense peer pressure from the natives and his obligation to act against his conscience to appear resolute and authoritative. He has no choice but to shoot the elephant himself or else risk looking weak and timid in front of the natives.