The immediate idea that occurred to me after reading how the narrator has used his “small rifle and poured shot after shot into [its] heart and down [its] throat” is: the elephant must die.
Although the narrator has confessed at the end that he “had done it solely to avoid looking a fool”, I find this explanation to be a mere concealment for a bigger crisis: the loss of his white/colonizer’s identity.
We can see this breakdown through a trajectory. At the beginning of the story, the narrator has evidently displayed anti-imperial sentiments, albeit guiltily. While already in a frantic mode of trying to detach himself from being a figure of the colonial “officer”, he is also quite equally bound to exercise the power endowed in him to subdue “the evil-spirited little beasts” with “yellow faces”. This ambivalence is further shown in his repeated declarations of not wanting to shoot the elephant despite having done so eventually.
This is where I see his identification with the colonizers being detached from him. One suggestion comes from how he has ‘unknowingly’ adopted the stance of a Burmese elephant: harmless when left alone, retaliates only when provoked. The point that I want to raise here is that he has already unconsciously identified himself with the elephant, although his ‘ego’ is blocking its entry into his consciousness. In other words, the narrator has unconsciously projected the workings of his own ‘id’ – here being the primal fear of death – onto the animal, thus his great reluctance at injuring it.
Yet, at the moment when he is suddenly made aware of his symbolic ‘double’, arguably through the sight of the elephant’s “great agony” and “powerless[-ness]” in which he has earlier professed, his ‘super-ego’ now propels him to eliminate the trigger of that epiphany – the body of the elephant as the ‘mirrored’ image of his now-unidentified self.
From the point-of-view of psychoanalysis, the elephant is indeed a doppelganger which is also the harbinger of death.