You waited until your kid was in high school to become aware that the public school is substandard?
BTW, The girl was an honor student and couldn't pass the same home school courses my daughter was taking. My daughter was far more advanced than she was and when they graduated, my daughter and her went to the same college and were roomies. She dropped out in 1 year and was pregnant in 2. My daughter graduated with a Bachelor degree in Poly Sci and a minor in Psychology.
It sounds to me this parent is just mad at the school and it would be a huge decision to take the child out of HS now. If the child was for it and not just talked into it, it might work. Home school kids learn to be self starters. If either the parent or the child think home school is easy peasy and doesn't need to be finished, they will fail and drop out. It is a MAJOR undertaking, but IMO, anybody can do it if they want it bad enough.
BTW, we used ABEKA and Saxxon math and loved it.