What is it technically about Christianity that makes it a subject that can't be taught in public schools?
Because it's real; because Christians believe in it, and will never say it's just a myth. It's a living religion (don't like that word), if you will. Satan would do whatever he can to stop it's spread.
Greek "gods and goddeses" are part of history (yes, so is our Christ, but He still lives) and so they can say they are teaching "historical religion". I don't think you'd find an awful lot of people around today who still believe those same gods or goddesses are/were real. They aren't a threat to anybody; merely carved images, idols....dead.
Gracey