Many feel that the accredited programs are not really home school. They call it public schooling at home. No real choices except which one to choose.
Many homeschoolers don't want the government, esp the public schools, in their homes. I'm one of them. If I had to go run to the public schools, or a governing body, every time I changed the way we did something, or if I wanted to try a new exciting program, I might as well give up and put them in public school. No thank you. I don't like the way they do it and I'm not allowed personal freedom under that plan.
Just how many deschooled, unschooled, eclectic/traditional, eclectic/unschooled, Charlotte Mason, Waldorf schooled at home, Montessori schooled at home people would take that offer...not many. We LIKE being our own child's teacher on our own terms.
But more than that, we see the choices we make as being an integral part of being the best parent we can be to our children, same as every other parent! Public school parents get that right. You can petition to move your child, you can move to a new location, you get iep's, doctors of education, testing and all you think is wonderful for your child. You have a choice! We want the same, a choice!
I see pushing parents to choose accredited programs as one more step the government is making to take my right to choose away and do it their way. If their way was in any way superior, that would be different, but it's not for my family and for thousands of others out there.
This isn't a matter if you are smart enough to teach Johnny to read, of course you are! It has everything to do with parental rights because the only choice we are given is one way. How is that a choice?