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Converesely, are the parents capable of conducting the home school? Do they have the temperment and training necessary? Home schooling a kid or kids is a significant contribution in time. You can't just say you're going to do this, and not commit a significant amount of your time to the task each day, and provide the structure needed.
Do you really understand the subjects, and are you able to convey them to others? It's one thing to be able to do something as simple as add, and quite another to effectively explain this to someone else, particularly someone who has a limited attention span. Schools, particularly universities, are jammed with subject matter experts who cannot communicate effectively.
What is the personality and mind set of the child? Do they need significant social interaction? In many cases, they simply won't get this at home. Will they take acadenic instruction as seriously from mom and dad as they would in a school?
We home schooled two of our kids for a while. Our daughter had serious health problerms, and simply could not keep up with the school structure. Our son, a year and a half younger, seemed to feel his sister was getting more attention, and requested home schooling. Both had been in a private Christian school prior to this, and, after a couple of years, went to a public school. Both were far ahead of their classmates when they returned to school, and remained so for several years.
My wife has a doctorate in what I'd call teaching teachers to teach (it has a formal name, but I can never remember it). I have a BS and MS in physics, with minors in math and computer science. We both taught some at the university level (particularly my wife) prior to trying home schooling. I still had reservations about our ability to teach subjects in which we had minimal background, but it should be obvious that we were probably slightly better qualified than some.
This is one of those areas in which I don't feel there is a universal answer, As stated previously, it depends too much on the circumstances. Given the circumstances we had, I feel we did the right thing. But this is something that no one can really answer for someone else. You are responsible for your kids, not someone else (perhaps especially third parties who really don't know the circumstances). You will need to make the decision, and live with the result. My wife and I wish you well in making a good decision.