Am I supposed to condense my entire view of education from primary to secondary school, and the relevant @home alternatives into a single paragraph? *sigh*
It depends.
It depends on so many factors that I honestly cannot give a straight yes/no answer. Except in one case: if you homeschool just so you can indoctrinate your child into whatever retarded cult you happen to follow, kindly go die in a fire.
Ok, real scenarios now. I suppose just about anybody is capable of doing at least a crappy job teaching elementary school material as the professionals, though then there's the issue of whether or not keeping a child that young from other children is beneficial in any way. I don't know the answer to that question, so I won't hazard a guess. I still remember being excruciatingly bored in elementary school, and I doubt I would have missed out on much if I had just stayed at home.
Ok, middle school. Now we're getting into matters of experience and knowledge on part of the instructor. Let's face it, not everybody can teach (that includes professional teachers as well). How would you explain elementary algebra, or the basics of science if you lack any background yourself? Yes, you could teach straight from the book, but that would make you a pretty crappy teacher. You will have to learn, a lot, and not just the answers to the problems from whatever book you are using. No, you will have to have a real understanding of the material. Again, I won't get into the whole socializing thing. I attended public school and turned out to be a veritable ass, so make of that what you will...
High school. Alright, now it's show time! Physics, math, chemistry, biology, geography, history, programing. Think you're up for it? In my high school, the teachers were required to have at least a bachelor degree in their subject, and some of them were still terrible! We're no longer at a point where feigning knowledge, or preaching from some textbook is sufficient. You have to have a real background now. Not some superficial "I took a class on it in college," but a real degree, and real experience. Without this, you're only holding your child back, and I'm willing to bet even farther than the public education system. Yes, you could still do this effectively, but you need to find other "teachers" with the necessary experience. I'd be very suspicious of any homeschooled college applicant whose parents did not hold at least one doctorate each. That social thing? Yeah, I was the awkward, kinda chubby nerd who always sat alone. Fuck that, I didn't miss out on anything anyway. Or in plain English, I'm not the sort of person whom you should ask about the importance (much less the desire for) of having a diverse social life in high school.
My father has a doctorate in electrical engineering, and my mother has one in chemistry. They are certainly more qualified than any (save one) teachers I've had, but that still wouldn't make them better at that job. I have two BSc degrees, and am currently in grad school for a MSc (followed hopefully by PhD). *I* am more qualified than a huge portion of teachers, and that still wouldn't make me a suitable replacement. My answer of "It depends" is really the only honest one I can give. There are loads of highly qualified people who simply cannot effectively teach, and there are tons of people who can easily get children to pay attention, but haven't got a clue about the relevant material. If you can make it work, great! If not, well, you're paying taxes anyway, might as well get the most out of it? I would like to stress though that I cannot recommend homeschooling past middle school. It's not for that bloody socializing claim, but because that is the point where real knowledge and experience are more important than anything else. Again, if you're a professor/Nobel laureate/Department Head, great! If not, please don't screw up another generation. Please?