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.