Why didn't the narrator want to shoot the elephant?
The narrator knew it was pointless, wasteful and cruel to shoot the elephant. The elephant had gone on a rampage in a bazaar, destroying some property, and had killed a man but now was calm:
And at that distance, peacefully eating, the elephant looked no more dangerous than a cow.
This male elephant had been going through a bout of must, a periodic surge in testosterone leading to highly aggressive behavior, but the narrator emphasizes that this particular spell has passed.
But beyond both practical reasons—to shoot the elephant is to destroy a valuable piece of property—and humane reasons (the thick-hided elephant would die slowly and painfully) the narrator doesn't want to shoot the elephant because in doing so he is acknowledging his powerlessness. The Burmese natives and their British overloads are trapped in an absurd, cruel system where they all play pre-determined roles. He must kill the elephant because the native people expect it, not because it makes sense:
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 . . .
Shooting the elephant clarifies to the narrator what he has become—a puppet—through participation in colonialism.
The narrator in Orwell's "Shooting an Elephant" does not believe that the elephant is dangerous. He realizes as he sees the elephant grazing peacefully in the paddy field that the elephant's period of must is over, and that the elephant now is harmless. He also knows that in Burma the elephant is a work animal and is worth far more alive than dead:
As soon as I saw the elephant I knew with perfect certainty that I ought not to shoot him It is a serious matter to shoot a working elephant.
Of course, the elephant had been dangerous. He wreaked havoc in the market place, killing one man. The narrator, a police officer, was asked to check out the situation. So, he picked up a gun that would at least make noise. But when he confronted the elephant, he knew what was what was expected of him by the crowd that had gathered behind him:
It was a bit of fun to them, as it would be tow an English crawed: besides they wanted the meat.
So, with thousands of Burmese behind him, as he held the gun on the elephant, the narrator felt that he could not back down, even though shooting the elephant was against his better judgment. Legally the narrator was right to shoot the elephant, but morally he was wrong. The elephant's death was unnecessary.