What do you think it is the reason for that? In other words, why do you think parents choose the classical approach over the traditional approach?
Traditional in the context of the United States.
I'm making the assumption that you live in the United States(22% of Steemit users are).
I think one of the reasons that classical education is chosen is a desire to provide a more in depth and holistic education than is seen in the traditional approach, as it is currently being taught in the United States. Parents want more, and classical style homeschooling is one of many educational styles they may adopt in search of that. For those who choose classical education they are reaching back into the roots of history in their quest to provide a richer and more rigorous education for their children. I am not a purist of any particular style myself, but feel that both history and modern science have a lot to teach us about learning.