Where's this kid's father? Or, even, just someone to say "No." and/or explain the facts of life to this poor kid.
Having raised a kid, and been around plenty of them in the process, I can't even imagine this topic coming up. Granted, I live in a conservative small-town, but the conversation, "Dad, I think I'm a binary gender" would uniformly be met with "Nope. You're not." and that would be the end of the conversation. The kid would grow up to be well-adjusted and happy, and life would continue on.
I would explain scientifically why they are incorrect. I’m a programmer and the binary switch is either on or off. There is no ambiguous in my world.