I'm not sure whether you're being facetious or are just incredibly uninformed, but the situation you're describing is only true of a fraction of homeschoolers and certainly has nothing to do with the chief advantages of homeschooling. The situations you describe are more typical of private schools, in fact.
Let me give you some of my background. I was homeschooled from kindergarten to high school (although the last three years of high school I took additional classes at a local community college). My family is deeply religious (and fairly conservative), but my curriculum incorporated teaching about all of the world's major religions, and in speaking to my public-schooled peers I have found that I know as much as if not more than they know about non-Christian religions. As an aside, several of my good friends in high school were bi- or homosexual; I read a number of books on evolution as pleasure reading in high school; and just a few months ago I attended a lecture by Dawkins. And what I've seen of other homeschoolers has indicated my situation is fairly typical.
As for advantages? Well, there is the flexibility. As I mentioned, I took around 50 hours of courses at the local community college, all while spending less time in schoolwork than any of my peers. (One person mentioned that even if you go to public school you're free after 3. Not true: Several of my friends taking multiple AP classes and going to magnet schools were up late nearly every weeknight doing homework. In contrast, I never once had to lose sleep to finish an assignment.) I was able to achieve quite a bit academically while focusing most of my time on my main interests--which, in high school, meant everything from playing guitar and keyboard in a band to reading extensively (Wealth of Nations and the first volume of Das Kapital in their entirety, for example) to teaching myself C++, Java, and several other languages.
Not everyone's going to want that, though, and that's fine. Let me tell you about my sister. When she was entering elementary school she was diagnosed with minor learning disorders (in addition to hearing loss, a speech impediment, and a few other issues); if she had gone through school as most students do, she would have been placed in a special ed program. My parents chose to home school her, and in eighth grade she entered a local public middle school. Long story short, she's now in the all-As honor roll at her high school, taking classes at a local arts magnet school, and having a blast in her school's marching band. I doubt things would have gone nearly as well for her if not for the flexibility and individual attention homeschooling affords.