You are free to believe anything about what the law should be, but the law does mandate secular education. (And properly so.)
Your argument is interesting, but the law is well settled.
It all boils down to taxation -- public schools are funded by taxes, and we all pay them. That includes Catholics, Protestants, Jews, Hindus, etc., etc., etc.
There is nothing so galling as being forced to fund somebody else's religion. Jefferson and Madison recognized that, hence the Virginia Statute for Religious Freedom, and the First Amendment. In their day it was the Baptists being taxed to fund the Episcopalians.
You're free to believe whatever you want, but you can't use my tax money to proselytize your religion.