I don't doubt it, but I think that those parents are simply abdicating their own responsibility to teach their children their faith at all. I just don't believe you have to homeschool to teach your children your faith. As you point out, homeschooling certainly creates different opportunities to teach faith, but I can't accept that non-homeschooling parents can't effectively teach their faith, and it seems that we agree on that point.
Children are missing out on a God-focused education for 6 hours per day, 30 hours per week.
I guess in my mind, teaching a child history or geography or calculus isn't part of a God-focused education. I see a distinction between the academic and spiritual aspects, and I see it as my role as parent (homeschooling or not) to teach my child how to fuse those two and include God in his life every day. I see the role of the school as educating my child in the academic sense (with my assistance, of course), not raising him.
How can parents form children when they have little control over their education?
I don't believe sending my children to a public school (or private school, or Catholic school, or any school) means I have "little control over their education."
Thirdly, because God is never mentioned in school, children learn either that: 1) questions regarding God are not worth studying 2) we don't study God because we can't know anything about God with any certainty 3) God is not related to important things like academics and career prep 4) people are hopelessly at odds regarding God so it's best that we don't even try to talk about Him 5) God doesn't exist 6) important stuff happens at school/ practice your personal religious preferences at home 7) important stuff happens at school/ home is just a place to hang your hat 8) society has determined that God is not worth discussing at school/ keep your personal religious preferences at home.
I think this is the real heart of our disagreement. Even if my children attend public school, my husband and I will be working to ensure that they do not learn any such ideas. I don't want them learning them from public school (or anywhere else... it is not as though public school is the only influence on a child). To the extent that school instills or even suggests them, they will be countermanded at home, and I intend for my husband and I to remain the pre-eminent influence in our children's lives. And I have a lot more than six hours per day with my children to exercise that influence. My goal is to build a strong faith in my children so that they can meet the challenges to it that they will face in the outside world, including the sort of attitudes you describe. I just don't see children absorbing the ideas you describe from attending public school, however.
Parents have the natural, God-given duty to instruct their children, not teachers.
I could not agree more. I just don't agree that sending your children to public school is an abdication of that duty on the part of the parent.
As usual, I'm getting to this thread too late but just wanted to respond to your post.
I guess in my mind, teaching a child history or geography or calculus isn't part of a God-focused education.
It certainly can be and should be. Just about every page in my children's science books begin with, "see how God made this..." Similarly with geography. This is less so with elementary mathematics, but in later years children should see the connection between eternal ideas (i.e., mathematics) and their eternal existence in the divine Mind. History, at the most abstract level, is the playing out of ideas in time. History demonstrates the consequences of bad philosophy. For younger children (and also for older children), history should include exemplary stories of heroic virtue.
I see a distinction between the academic and spiritual aspects,
This is a false distinction, and a very serious mistake. All academic studies point ultimately to God.