The beauty of homeschooling is that you can tailor it to fit your children, your family and your community. Like moominmama stated in a pp, you can teach your children based on their actual level, not on their grade. School has some flexibility but is ever focused on the middle. This can leave kids who are otherwise perfectly normal feeling like they are somehow deficient when quite often it is nothing more than lack of readiness. And kids at the top can find that a ceiling exists for them, too, within the school system. Homeschooling can address all these issues with a flexibility that schools are incapable of, and no two families will look alike in their approach. Some will be more secluded, either by choice or situation, others are hardly ever at home and use the community resources liberally. So to say that kids being with parents and siblings most might be true, but is usually the preconception that schoolers have about homeschooling in general: the "school-at-home" model.
It is regretful that parents choices are limited regarding their kids. Most of us only have two options, if that: homeschooling or public school. I know I could not get a job that would make private school, or even preschool, a good financial option. I wish there were more cooperative learning schools that could follow child-led learning but without specific demands on kids. Or, just like the variety of homeschooling styles, have schools with varying amounts of demands, from rigorous to completely open (and public!). If only! Then parents would have a true choice to fits their needs and their child's.
The fact is that most parents would still choose school over homeschool, and it's nice that "free" education is available. Unfortunately, my experience has been that most parents choosing this option just can't wait to be rid of their kids for the day, and are not choosing it for any notion of superiority over the homeschooling models. Fewer are the parents I meet that regret not being able to homeschool due to financial constraints. PPs addressed the rest of this issue, so I won't "retread the thread"!