In the final paragraph of his essay, "Shooting an Elephant,"  George Orwell gives a description of the reactions of the unnamed protagonist's fellow officer's to his (the character's) killing of an elephant that allegedly went mad and trampled an Indian village woman. Orwell says:

Afterwards, of course, there were endless discussions about the shooting of the elephant. The owner was furious, but he was only an Indian and could do nothing. Besides, legally I had done the right thing, for a mad elephant has to be killed, like a mad dog, if its owner fails to control it. Among the Europeans opinion was divided. The older men said I was right, the younger men said it was a damn shame to shoot an elephant for killing a coolie, because an elephant was worth more than any damn Coringhee coolie. And afterwards I was very glad that the coolie had been killed; it put me legally in the right and it gave me a sufficient pretext for shooting the elephant. I often wondered whether any of the others grasped that I had done it solely to avoid looking a fool.

The unnamed officer's peers are divided between older officers and younger officers, and each group holds opposite opinions to the other. Where the older officers assure our protagonist that he was in the right for putting down a potentially dangerous animal, the younger officers believe that it would be better to let the animal live. As for who is right and who is wrong, it comes down to a basic interpretation of the text and the morals of the individual reader.

The younger officers are, indeed, difficult to sympathize with, considering their extremely prejudiced language. They say quite explicitly, "an elephant was worth more than any damn Coringhee coolie,"  meaning that the elephant was more important than the native person that it had killed. However, when looking at the text as a whole, and the hatred and prejudice that the officers experience at the hands of the Burmese people (in the beginning of the text, Orwell explores the cruelties enacted by the natives in reaction to the very strong "anti-British" feeling in the area), we can understand the reactionary emotion behind it. In addition, Orwell's character states, "as soon as I saw the elephant I knew with perfect certainty that I ought not to shoot him... [a]nd at that distance, peacefully eating, the elephant looked no more dangerous than a cow. I thought then and I think now that his attack of "must" was already passing off; in which case he would merely wander harmlessly about until the mahout came back and caught him." However, pressured by the Burmese people who had been the cause of many of his torments, the protagonist has a strong desire to appease the natives, and kills the animal anyway.

By contrast, the older officers had spent more time in the area, dealing with these people, and therefore had a better sense of how to remove themselves from the emotional aspects of the job. For the safety of the officer (and to make the job easier), it is a wise decision to gain the trust and respect of the people under their protection. And as the elephant had already killed a man, it was the right thing to do to put the elephant down. As for which is the correct approach, or who was in the right, the question simply boils down to the audience's moral code and interpretation of the text. The fun thing about literature is that there is rarely a single "right" answer, so long as you can back it up with evidence from the text.