Why? Answer: Two reasons.
1) Godless government schools aren NOT religiously neutral in content or consequences. In fact, the children must learn to think and reason godlessly just to cooperate in the godless classroom. How could it be otherwise?
And...
2) God-centered government schools aren't religiously neutral, either. Whose religion? What religious texts? Whose religious leaders will be cited? OF course, children of atheists shouldn't be under police threat to subject themselves to a government sanctioned religious worldview.
Fundamentally, government schooling was a bad idea from its very beginnings. **ALL** of them are a First Amendment and freedom of conscience abomination! ( Yes, I do mean, “all”).
The 1787 Northwest Ordinance, which predated our constitution, set aside land for schools and declared:
“Religion, morality, and knowledge, being necessary to good government and the happiness of mankind, schools and the means of education shall forever be encouraged.”