I'm an atheist, and yet I have read the Bible completely through more than once. I own several, and still refer to them from time to time -- as I do to my Homer (Iliad and Odyssey), Virgil (Aeneas), Dante (Divine Comedy), Lee (To Kill a Mockingbird), Shakespeare (too many titles to list) and Doctorow (Ragtime) among many, many other cherished favourites. If anybody truly wishes to know who we (humanity) are, then they must read what we collectively has thought and written.
I have no difficulty with that -- if an English high school class can learn Harper Lee or E.L. Doctorow, then they can learn the Bible. And -- with this one caveat, that it is expressly called "Literature" -- the Upanishads and the Bible. (Cant' get through Upanishads myself -- they bore me -- but love the Epic of Gilgamesh, in which Noah, under the name of Utnapushtim, appears.)
See? Learning is a good thing -- even learning what people believe. Just so long as you are learning and not being indoctrinated. In any case, for those kids taught Bible inerrancy or literalism at home, you won't get them to believe it's fiction anyway -- too late for them. But even so, so what? As long as you teach that these are "stories," that they are "our stories," I say go for it.
The good thing is that it is not to late for those who have been taught or have come to believe the stores are not true, still have some time, it they have an open mind.
Telling children the stories in the Bible are not true, is like telling them Santa Clause is real.