I've read this book twice. The older copy from my library was so helpful that I purchased the newer one and read it too. I just spent some time reading the 1-star reviews of it and find myself thinking, "These people just don't get it." First of all, you shouldn't take on anyone's homeschool philosophy whole-heartedly without researching and evaluating yourself and your kids. Also, the book does not claim to be Christian. In fact, the chapter on Bible specifically mentions that they are not going to presume to make your religious/faith-based-education choices for you.
Most importantly though, this is a how-to on classical education. The opening chapters say that yes, it's strenuous, yes, it's language oriented. It will be focused on reading, writing, and discussion. And I fail to see how anyone could say you get a shell of an education when the same topics are covered three times with increasing thought given each time. The whole purpose is to introduce ideas and then analyze them.
The authors introduce these ideas and expect you to analyze them too.
Use your own thinking here. If you want to introduce faith AND analytical thought, just teach your children about God's truth AND greek philosophy. We have been studying Egyptian gods this week with my first grader, and she completely understands that there were people with a different way of thinking and that they did not know and worship the one true God. (In fact, of her own thinking, she reasoned that they would not live again in heaven and was very sad. I wouldn't have intentionally addressed that at a young age.) Teaching the ways of other cultures does not water-down faith and it doesn't worship the Greeks, as some critics said.
Also, if the time schedules don't work for your family, don't sweat it! You can teach this method without following the authors advice to the letter! Every home school is different and completely customizable. That's the great thing about it.
I love the ideas behind this book of exploring a topic at early ages, analyzing it at the analytical age, and expressing your own genuine thought at the creative age. So different from my own education where we were not encouraged to have analytical thought until upper level high school.
It's definitely worth a read. But not a hard-and-fast rule for everyone.