Shooting an Elephant is told in a naturally assumed first person point of view. Perception of the police is negative, they are the symbol of an imperialistic government...... thus, the police are a symbol of an unjust government, and the police themselves symbolize power to the people.
The elephant in the story represents the people....... and the policeman does NOT want to destroy it. The objective here, would be for the policemen to gently guide the beast back to his path....... If you look at this in terms of the people, the police see themselves as gently guiding the people and showing them mercy. The people, on the other hand, don't want the elephant shown mercy. They want to see his death............... this represents the people's need for a government that controls them. They want the elephant controlled, and they want themselves controlled.
This might make a bit more sense to you if you look at in terms of our own need in the United States of strong leadership. We expect our president to step up and take control if a situation warrants it...... we don't live in Burma........ we don't want anyone to kill the stray elephant on the street, but we do want to know that in an emergency we have strong leadership, and a strong military to back it up.