*Note: I do not endorse everything that the American Vision teaches. In fact I'm not sure how much I even Like their ministry. But I must concede that I am in agreement on their optimistic Postmillennial approach.
This is about as simple as it gets. To many this simply sounds like "take your children away from places where they will learn evil things". But that's not the case at all. I shouldn't mind my children learning about evolution when the very culture of the world is being poured into them by the gallons. Why should I worry that our public schools don't permit public prayer when the children are being inundated with materialism and sensuality? We are straining out the gnat and swallowing the camel (Matt 23:24) in our attempt to teach morality.
This is about something much bigger that morality. This is much bigger then sheer knowledge. Thus is not about what things they are learning but what worldview they are learning. There is principally no difference between math and science in either school option (Christian or Secular) but the worldview is far from the same. It isn't the morality of opening a lesson with prayer but the knowledge that the person educating your children humbles them self before God before teaching. It isn't the practice of prayer that makes your child holy but the repetitive acknowledgment of Him and Him alone as the source of ultimate truth. This is not about Scientific opinion. There are plenty of conservative "Bible believing" Christian Scientist who accept an old world view, a non-literal six days and perhaps even hints of macro evolution. But they see any and all approaches this scientific information takes as conforming to a Biblical worldview.
Parents often fret over who their child spends time with and which house they go over to but they don't acknowledge that they send them to the world's playground for a majority of the adolescent life. These children for the most part are not strong enough in the faith to withstand the pressure of society (resulting in a growing congregation of atheism on college campuses). Heck many of these children's parents aren't strong enough in their faith to withstand the pressures of the world but somehow we want to cling to the "in the world but not of the world" mantra.
I won't go so far as to argue that all Christian children should be home-schooled. But if we take seriously that bad company corrupts good character (1 Cor 15:33) then we are foolish to live like we are immune. Being "in the world" is for the mature. We can't send our children to places where they are being taught to love the world and not expect disaster (1 John 2:15-17). As the video states, this equates to sending them back to Egypt.