The same struggles and influences are to be found in Christian schools as are in public schools (yes, possibly to a lesser degree, and with diminished regularity). But there is no guarantee that this is the case.
Obviously there is no guarantee of anything, but there is at least an increased probability. Since all these kinds of decisions are based on probabilities, why would one not go with the best odds?
Yes, but it’s silent in matters of mathematics, grammar, and biology. The fact is that these subjects (though grounded in the Living God) are not particularly or exclusively Spiritual, and the Scriptures are silent regarding them.
On the contrary; I think every subject is related to God in some way. What makes mathematical truths, true? How does eternity relate to time? What are the purposes of living things? Where did they come from?(!) What is the best way to use one’s words? Further, given what God says about the purpose and nature of children, what pedagogical methodologies for teaching these subjects would be best? Answer any of these questions, and eventually God is related. And further, nothing in the Deuteronomy text limits the education to “Spiritual” matters. Even if it did, the question would be: what parts of the world is the Holy Spirit not related to?
Of course, it’s not as if every word coming out of the instructor’s mouth must be “God” or a quotation of scripture. But I think the previous point is true, notwithstanding.