For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
These two verses talk about teaching children,
Proverbs 22:6 ESV
Train up a child in the way he should go; even when he is old he will not depart from it.
Deuteronomy 6:5-9 ESV
You shall love the Lord your God with all your heart and with all your soul and with all your might. And these words that I command you today shall be on your heart. You shall teach them diligently to your children, and shall talk of them when you sit in your house, and when you walk by the way, and when you lie down, and when you rise. You shall bind them as a sign on your hand, and they shall be as frontlets between your eyes. You shall write them on the doorposts of your house and on your gates.
Schooling has moved on from the Old Testament days and unless the parents are actual teachers then children should go to school. There are some good Christian schools around where Christian values and Bible education is taught but these schools are not always available to all.
The biggest and hardest subject to counter is evolution in science. Christians believe in creation which is diametrically opposed to evolution. It will take sensitive teaching from parents to counter this evolution myth.
To me this is really the only stumbling block that would lead me to teach my children at home.
As in all things we should pray and ask Gods guidance whether homeschooling is the right way for our own family. We will ultimately have to answer to God about how we raise our children but as long as we keep our children educated in the Bible, Gods word will speak to them.