On the other side, he was conflicted because he did not want to shoot the elephant just because he was expected to. I see a certain amount of irritation and being forced by circumstances into a course of action he did not want to take.
The biggest motivation that caused Orwell to shoot the elephant was a curious combination of personal and political motives. What made him shoot the elephant at the end of the day was the fear of being laughed at if he did not. As he was a representative of the British Empire, which, by its very nature, could not be laughed at, he felt constrained to shoot the poor elephant.
A key component of Orwell's motivation was political. He felt trapped, or cornered (like the elephant), by the colonialist governmental role--he felt like his hands were tied and that he must act as the representative of the British government instead of as an individual person of conscience. Therefore, he felt combined external pressure and expectation compelling him to shoot the elephant.
There is certainly a component of circumstantial motivation to Orwell's actions here. Never before this moment had he considered shooting an elephant, and, though he did it, it is only because of the pressure he feels at this moment to do so. He is not comfortable with anything about this whole incident, which makes it clear that his motivation is peer pressure--although those around him are not his peers. If he could have just walked away, he would have.
I think it was mostly a mix of personal and political. Orwell did not want to look weak personally, so he shot the elephant. But one aspect of not wanting to look weak was definitely political. He felt that if he looked weak, it would reflect badly on the whole British colonial establishment in Burma. So, for him, the personal and the political were definitely intertwined. I would argue that the political was more important, but they were certainly both there.