The story is in the second person because the kid is talking to himself. There is no good reason for this. He’s not having an out of body experience. He hasn’t had some grave trauma that causes him to distance himself from himself. He’s a kid. His parents are divorced. His stepfather isn’t even that big of a jerk. Second person is a gimmick.
In the interest of fairness, another read on “Leopard.” This post is a bit too belligerent, but things get more nuanced in the comments and the blog as a whole is pretty smart and together.
Meanwhile, Wells Tower explains why he chose second person here. Basically, it’s the same reason most fiction writers seem to give for anything, including writing — he tried the other options, and they didn’t quite cut it, so he went with what felt best.