It is our ministry to raise and teach our children the way of the Lord.
Deuteronomy 6:4-9 Hear, O Israel: The Lord our God, the Lord is one.5 You shall love the Lordyour God with all your heart and with all your soul and with all your might.6 And these words that I command you today shall be on your heart.7 You shall teach them diligently to your children, and shall talk of them when you sit in your house, and when you walk by the way, and when you lie down, and when you rise.8 You shall bind them as a sign on your hand, and they shall be as frontlets between your eyes.9 You shall write them on the doorposts of your house and on your gates.
Read chapter 5 it is the giving of the 10 Commandments, we need to teach our child the 10 Commandments, why?
Romans 2:17-24, 3:19-20 But if you call yourself a Jew and rely on the law and boast in God18 and know his will and approve what is excellent, because you are instructed from the law;19 and if you are sure that you yourself are a guide to the blind, a light to those who are in darkness,20 an instructor of the foolish, a teacher of children, having in the law the embodiment of knowledge and truth—21 you then who teach others, do you not teach yourself? While you preach against stealing, do you steal?22 You who say that one must not commit adultery, do you commit adultery? You who abhor idols, do you rob temples?23 You who boast in the law dishonor God by breaking the law.24 For, as it is written, “The name of God is blasphemed among the Gentiles because of you.”
19 Now we know that whatever the law says it speaks to those who are under the law, so that every mouth may be stopped, and the whole world may be held accountable to God. 20 For by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin.
The 10 Commandments are the foundation of Christ, they are the embodiment of truth and knowledge, what do they bring knowledge of "sin". Unfortunately many people that name the name of Christ do not know how the 10 Commandment pertain to their lives. They bring us to the knowledge of sin and they guide us in our walk with the Lord, the Law of liberty, sweeter that the honeycomb. We as parents need to teach our children, not a christian school the ways of the Lord. Many christian school have the same problems are public schools the only difference is the indoctrination. Public is worldly and the christian school should be Godly, but there is no guarantee that they will teach your children these things. Here's the sad part is parents spend all that money to give their children a good education and shield them from the world. Then they go to college and get shell shocked because in any school not everyone in a place of christian education are christians.
As all as you do your part to teach your children I don't see a problem with either. The children will be exposed to the world sooner in public schools as opposed to christian school.