A few years ago I read a fantastic book on education titled A Thomas Jefferson Education. This book and Every Child has a Thinking Style are two books I recommend to any parent when considering their children's education. Neither are pro-homeschooling or pro-public education and so not likely to offend.
Our children are unique and wonderful and blessedly different from each other. We have a child who is brilliant at math but just learned to read at age eight, a four year old who uses big words and explains complex thoughts to us, a ten year old who devours books and reads at a college level, a six year old who likes to correct the textbooks.... and those are just some of their intellectual characteristics. Throw in the jumble of diverse personalities and we have really got a mix. This is one reason we teach our children at home.
From experience, we know the challenges our children would have faced in a one-size fits all classroom. This is not an insult on any teacher; this is us knowing our children and their personal bents.
Along with giving our children a Biblical world view, we also want to give them an accurate world view. I won't weigh this down with links, but you can google "how many errors in textbooks" or something to that effect and see that history and science are being taught differently, inaccurately. Politial parties change and influence the content of public school textbooks to fit their agendas. They know what conscious parents know - that children are moldeable and pliable. This is another reason we teach our children at home. We are able to research and use trust-worthy resources.
As I mentioned, each of our children have a natural bent, and as they learn at home, they are allowed the freedom to pursue a subject that interests them and drink of it as long and as deeply as they like. We have a weaponry and arms expert living under our roof. As we read about the Civil War last night, he ran to grab one of his books and show me two pistols that belonged to Abraham Lincoln and explain in detail to me how they worked. Another child is gifted mechanically. He put together a table set for a friend when he was two, takes apart any cast off appliance and shows me how different parts of it work, often reassembling the parts with his knex or legos to make a moving vehicle. Now our kids aren't geniuses and they will, most likely, have regular lives, but they have been given the freedom to love to learn. This is another reason why we let them learn at home.