Orwell flatly does not want to shoot the elephant, which, after rampaging through the bazaar and accidentally killing a man, has calmed down. He is forced to by the expectations of the crowd, before whom he can never appear weak. This is really the point of the story, that the relationship between the colonizer and the colonized is fundamentally corrupt. Orwell sympathizes with the Burmese people, but they hate him, because they see him as little more than an instrument of empire, which they associate with violence and oppression (what Orwell calls the "dirty work" of empire.) Yet they also expect him, as a dispenser of legitimate violence, to take vengeance on the elephant by killing it. He really has no choice. The situation calls for him to behave with cruelty, because that is the only way he can fulfill the expectations of the Burmese townspeople, and maintain sime sense of credibility in their eyes. On the other hand, Orwell is glad, he says, that the elephant had killed a man, because it put him legally in the right by shooting the beast. The incident puts Orwell in a predicament, one that is unique perhaps to colonialism, and one that could only be resolved by cruelty.
In this essay, Orwell has very negative feelings about shooting the elephant for a number of reasons. First of all, he knows that this elephant is just having a "must" and will eventually calm down. Secondly, he notes that it is a "serious matter" to shoot a working animal because it is the equivalent of destroying a very expensive, and very important, "piece of machinery."
In addition, for Orwell, shooting the elephant is the same as committing a murder. He has never had any desire to shoot such a large animal and, as he observes it in the field, he says that it has a sort of "grandmotherly air" to it. This implies that Orwell does not want to shoot the elephant because it has almost human characteristics.
Finally, Orwell states that he is a "poor shot with a rifle." In other words, he knows that if he takes a shot, he is likely to either miss the animal completely or simply wound it. This would cause immense suffering the for the animal. Incidentally, this is what happens: Orwell shoots the elephant, the shot is not fatal, and the animal dies slowly.
Despite Orwell's strong feelings, he must shoot the elephant. It is what the crowd expects and, more importantly, it is what imperialism demands.