Thanks so much for all the comments, ladies!
Here's some further information on the trend I'm noticing: it is specifically that character training is a subject, like math or reading, and that it is the most important subject. That is what I'm disagreeing with, because I don't think character can be taught as a subject. At least, I can see that it can, and maybe that should be a minor part of forming a child's character (after all, it's easier to try to be patient if you've been given a definition of "patience"), but I don't think it fits under the umbrella of "school" nearly as well as under "parenting" for the simple reason that most of our character development comes from what we see, do, and imitate.
School will be part of that, just because it's part of our day, but I don't think that character development is more particular to school than it is to, say, chores.
I suppose, when I look at school, I would say that the primary duty of a Christian teacher is good academics, just as the primary duty of a Christian carpenter is producing a good table (thank you Miss Sayers!). In other words, if you let the academics slack because you're more concerned about a nebulous "character issue", you're actually having the opposite of your intended effect: you're producing a lazy, ignorant student.
But . . . I can certainly see viewing homeschooling as a weapon in your parenting arsenal. Much as you might use a chore chart to help produce diligence, you can use your schooling method to produce, well, diligence. :) And family closeness, and opportunities for Bible study, and on and on. That does make a lot of sense to me. What doesn't make sense to me is seeing the primary purpose of homeschooling as character development. I should think that the primary purpose of homeschooling is education - the primary purpose of any form of schooling is education. Now, the reason you most value education could well be character development. And you could certainly think that homeschooling, properly pursued, is more conducive to good character development than other forms of education. But I think if your schooling aims at a good character, you're not going to get it. But if your schooling aims at a good education, you will get that, and likely get a good character thrown in (if all the other necessities are in place, of course).
That said, as Kelly and Elena both pointed out, you can homeschool for developmental reasons, especially in the early years. I'd put my family in this group; we first started looking into homeschooling when we realized that public school would mean our five-year old would be out of the house for about the same amount of time my husband was at work! We honestly think homeschooling is better for our family dynamics (less stressed mom and kids!) right now. And that is connected to character - stress can lead to growth, but too much stress can stunt growth. But again, I would say that was a parenting decision . . . homeschooling was the right tool for the job (sometimes you want a Phillips screwdriver instead of a flat head screwdriver).
But it was also what you might call an economic decision: I didn't think what we'd be getting would be worth what we'd be paying for it. I don't think that eight hours a day of my child's life is worth the return of an education that lacks history, foreign language and religion. So the fact that my child would be unduly stressed was part of it, but also that she'd be unduly stressed and uneducated. Not worth it. Because, again, school should produced educated children.
Amie, I appreciate your point too, that Christians can educate better because we have the truth. I agree, actually. But I don't think that this is something that's impossible for Christian public school parents to do (I don't assume you do either!); there can be a lot of benefit from having teachers who disagree with you and then coming home and discussing it all with your parents, and having them help you form good arguments to support your own beliefs. Those parents are also educating Christianly, they're just doing it in a different manner.
So, in this particular case, it was literally the idea that the character issues I'm working on with my child (honesty, kindness, etc.) should be written down in my lesson plan book along with her math assignments. I just think it's miscategorization. I think those things exist alongside schooling, but if I had to categorize them, I'd certainly put them under parenting, and not schooling. I think that including them in schooling (perhaps unknowingly) assumes that public school parents couldn't possibly be discipling their children too, because it assumes that school is primarily about character growth, and not about education. (Again, if I'm cooking, I should be a good person while I'm cooking, sure, but when it comes to the job itself, what matters is not my character but how the chicken tastes!)
So, education certainly impacts character, and visa versa. But nothing in life is really unconnected to anything else, and just the fact that they're connected doesn't mean that they're in the same category. Huh. I suppose when it comes down to it, my frustration is really that I'm using the Dewey decimal system and they're using Library of Congress!
(I.e., you're right, Amie, I should just ask more questions.)
Thanks again for the discussion; I'm very open to hearing yet more thoughts on the subject.
Peace of Christ to you,