I am interested in giving my children a classical education because I think that in order to understand the present, you have to understand the past. This goes even further than just knowing history, although obviously I think the history-centric curriculum is great. I particularly enjoy how the history is not disjointed, the way it usually is taught in schools, with entire continents ignored and huge gaps.
As for the other subjects, I guess I'm just a traditionalist. Learning Latin teaches so much about English. Logic and rhetoric teach us not only how to get our points across, but also how to understand the points that other people, both past and present, make. All the nitpicky stuff that has been taken out of so many public school curricula, like grammar and spelling and music appreciation and art criticism, lead to a deeper and richer understanding of the world. We are not religious, but by teaching our children about the religions of the world, and what they believe, and their texts, we help them to understand history, art, and literature.
A classical education obviously isn't for everyone, but I think it will turn out the most educated child that can reasonably be expected. Now, the trick here is that there are all sorts of things that "educated" could mean, and that's kind of the point... all homeschool parents have to pick out the program or ideology that they think will best prepare their child for the world. So I guess it depends on how you see the world!