Why don't the churches and schools teach about the Anunnaki who are mentioned in the Bible as the Sky People who created the Neanderthal? ?

Because of the lock-down. 

maybe theyre too busy teaching everything else

Your pants are on fire, sire. 

Where in the Bible is the Anunnaki mentioned.  It doesn't matter to me not being a Christian or a Jew, I just don't see any mention of Anunnaki in the Bible.

Because, Dollface McCupcakepants, that is the collective name for gods featured in the mythologies of Sumerians, Akkadians, Assyrians and Babylonians. The accounts of them are contradictory, but basically, the top gods, the big cheeses, the cream of the cream. 

So teaching about them would take place in world mythology classes or ancient history classes where you're studying things like the invention of agriculture and how we domesticated pigs and the invention of cities. 

Now, you might have fun tracing the individual gods and goddesses to characters in the Bible...oooh, fun. Play detective a bit. Esther, for instance. 

Trying to ascribe the Anunnaki as 'creators' of the Neanderthals is...LAUGH OUT LOUD ACTUALLY FUNNY AS HELL. I giggled. A lot. It's, uh, high nonsense and crap on toast, baby. 

Because they don't have the keys to the Kingdom of God, clearly.