There are 3 main types of schooling in America.
1. Public schools -- These are schools funded by public sources such as taxes and lottery earnings, etc.. They are often portrayed as crime ridden and failing in educating but this is often a function of the community they are in. Poorer communities tend to have poorer public education systems. It does have the advantage of socializing that other types of education lack (more on this later).
2. Charter / private schools -- These are schools that derive their funding from private sources such as tuition or through vouchers for poorer families. In the case of religious private schools, they also concentrate on their religious teachings as well as the standard curriculum. You find these in richer communities and they have the advantage over public schools because they can pick and choose whether the student will attend. Many see them as siphoning out the best students from the public school system and reducing the resources availible to public schools.
3. Home schooling -- This is where the student is taught at home for various reasons (some valid, some not) mostly for the reason of the perception that the previously mentioned types do not suit the needs or beliefs of the parents. The difficulty with home schooling is one of credentialing and certifying that the state approved requirements are being met. Home schooling requires a much higher degree of involvement on the part of the parents which often can't be the case due to the necessity of having both parents working to make ends meet. You do mostly see home schooling being done by parents who either have a high degree of distrust in the public forms of education or have a religious reason. Lastly, there are some areas that are remote or that have extreme weather conditions where home schooling is the norm. But these circumstances are fewer in the US because of the extensive network of public / private schools available and public funding of busing.
Personally, I think home schooling is a bad thing for kids since it doesn't teach them the proper socialization they will need as adults. It is often done for all the wrong reasons in all the wrong ways which can and often does hold the child back making things worse for that kid. And as the poster of this article has noted, it does tend to be the parents that can't let go of their offspring that want to keep them home all the time. This is unhealthy IMO. I personally believe that home schooling should be the choice of last resort since it does require a much higher degree of commitment from parents which often can't be met especially in poorer communities.