I doubt I will change your mind on this issue. But the thing about home schooling is that as a parent you're given a great amount of freedom and latitude. With that freedom you can either produce really good results or really bad ones (like your example). There are religious communities in the midwest who home school their children but don't teach them how to do basic arithmetics, and have them memorize bible verses. Many of the kids can't even spell their name. Does that mean home schooling is bad? No. It just means their execution or implementation of home schooling is poor. The best implementation of home school is when a parent supplements their child's core education with socialization (i.e.: taking trips with other home schooled children, joining the local school's sports team, etc.). School isn't the only place in the entire universe where one can develop their social skill.
The public school system is just a school-to-prison pipeline for minority students (
http://en.wikipedia.org/wiki/School-to-prison_pipeline). Government-run schools are not interested in educating children (especially black children). They just want us smart enough to be worker bees. They discourage creativity, individuality, and critical thinking. We're trained to sit still and take orders.
Here's a TED talk of a 13 year old who quit school: