Your question suggests that teaching Christianity to children is not decent education, and is not real history and does not have reputed academics behind it. All three suggestions are incorrect.
In most countries, education is managed by the state, and is paid for by taxes. Some people for faith reasons, and also for other reasons, will homeschool their children, and those who can afford it will send their children to parochial schools, but the majority of people use the schools that are provided by the state.
But if you are asking why a Christian would not provide their children an education without God, and without teaching them about Christianity --
Supposing a parent said to their children: "Because I love you, I am not going to give you some healthy food, I will give you junky food that will not help you grow healthy, and I will give you a choice to pick out what you want."
People, particularly adults, tend to do the things that in their estimation will bring the greatest value for them.
Most parents provide to their children the very best that they can give them. Faith in our Creator and in Christ will guide them throughout their lives to do good and to be productive, and to have a purpose and a hope for the future.
(Proverbs 2:10-13, 20-23)
10 When wisdom enters into your heart and knowledge itself becomes pleasant to your very soul, 11 thinking ability itself will keep guard over you, discernment itself will safeguard you, 12 to deliver you from the bad way, from the man speaking perverse things, 13 from those leaving the paths of uprightness to walk in the ways of darkness.
20 The purpose is that you may walk in the way of good people and that the paths of the righteous ones you may keep. 21 For the upright are the ones that will reside in the earth, and the blameless are the ones that will be left over in it. 22 As regards the wicked, they will be cut off from the very earth; and as for the treacherous, they will be torn away from it.
Too many children who are not given any hope for the future will resort to drug addiction and make some very bad choices about the life that they live. This is not because they don't have a choice, but because they do not have sound role models in their lives, and will succumb to peer pressure. Christian parents are commanded by God to be positive role models for their children and to teach their children about God. (Ephesians 6:4)