Some philosophers dismiss this as a question about a tautology: when Alice asks "Why am I Alice?", this is equivalent to her asking "Why is Alice Alice?", which is not an interesting question. But other philosophers believe that, from a first-person perspective, the question is nontrivial. For example, Benj Hellie, who calls it the vertiginous question, writes in this paper:
The Hellie-subject: why is it me? Why is it the one whose pains are ‘live’, whose volitions are mine, about whom self-interested concern makes sense? That thing there in the objective world: what is so special about it? Why doesn't some other subject of experience there in the objective world ‘go live’ in this way: for instance, the ‘Chalmers-subject’ out there driving around in the human being whose visage matches a photo on a certain driver's licence bearing the name ‘David Chalmers’—why not instead it?
More examples: JJ Valberg expresses a similar question in his book Dream, Death, and the Self, as does Mark Johnston in his book Surviving Death (page 151, "Am I Now Contingently Johnston?"). In this paper, Vincent Conitzer draws the analogy to a world simulated on a computer, where the perspective of one of the creatures in the simulation is displayed on a screen in our own world. He argues that, beyond the code responsible for the simulated physics, there must be additional code that determines which creature's perspective to display, so that there is a further fact, in addition to the simulated physics. Caspar Hare explicitly proposes a metaphysical theory (egocentric presentism) in which one single person's experience is distinguished as the present one. Closely related ideas appear in this paper by Giovanni Merlo.
Interestingly, David Chalmers (page 85 of The Conscious Mind) seems to recognize the question as nontrivial, but he also seems to think that it is not that problematic for a materialistic worldview:
[...] the unexplained fact [that David Chalmers is me] is so "thin" by comparison to the facts about consciousness in all its glory. Admitting this primitive indexical fact would require far less revision of our materialist worldview than would admitting irreducible facts about conscious experience.
So, Chalmers seems to think that this is less of an issue than other philosophers who accept that the question is nontrivial. I am not sure that I understand his position. How, exactly, would we revise our worldview to admit such a fact? Are there other possible responses to the question or ways to deal with it?
Update in response to answers: Of course much depends on what the "I" in the question refers to. If it refers to the human being in question, then it does seem tautological, so those who take the question seriously presumably take it to refer to something else (a transcendental self?). Alternatively, the word "I" could be removed from the question altogether; for example, "Why is this particular human being's perspective present?" (along the lines of Caspar Hare's theory, above). Are there other options?
Please note that this is not a question about personal identity over time (what makes a person at time 1 the same person as that person at time 2); though such questions may be related, the question here concerns a single point in time.