This system has three primary goals. First, to train thinkers, entrepreneurs and statesmen-individuals with the character, competence and capacity to do the right thing and do it well in business, government, church, school, and family. (though I'll reverse the order)
The second goal is to perpetuate freedom, to prepare people who know what freedom is, what is required to maintain it, and who exert the will to do what is required. These two goals are accomplished by the third: teaching students how to think. Those who know how to think are able to lead effectively and are able to help society remain free and prosperous. The success and perpetuity of our society depend upon leadership education.
My take on this:
While I agree with DeMille's worldly view to a point, I'll go further and say that to be a real leader we have to train our children to learn from the Greatest Leader that ever is. Without Him, we can do nothing. We have to train our children to be leaders where God put them, to preach His Word for His Glory.