Well I suppose I am uniquely qualified to comment here since I was actually homeschooled for 6 years. Obviously there are advantages and disadvantages to it. I don't think kids should be homeschooled just to be homeschooled. There really has to be a specific reason. You certainly don't learn as well at home by yourself. I struggled a lot with things like math and science where I didn't have a teacher that was well versed in stuff like that. You are also missing basic things that schools easily offer such as knowledgeable teachers, other students to bounce things off of, gyms, sports teams, science labs, connections (meeting people) etc.
On the flip side, when I went to school (K-6th) I was very good at things like math and taking tests and stuff like that. A lot of that doesn't mean much in the real world. However I did lack a sort of literary/artsy side that wasn't practiced much in school, at least the ones I went to. Things like how to write something weren't talked about much but I sure knew how to do something useless like diagram a sentence. The things I was good at or struggled in sort of flipped when I was homeschooled. I seemed to gain a little more of an ability to be independent and do things on my own rather than having to rely on others.
All of you union and PC bashing people here can say what a drag our school system is but most people I know that are my age and younger are certainly book smarter than me. They all know how to do calculus and physics etc. I barely was able to pass algebra 2 immediately after high school at the community college. There are some things that are much easier to learn from a teacher than trying to learn it on your own.