Complaint about homeschooling: Socialization
One of the critiques that homeschoolers hear, and voice their frustrations over, is that their children, by virtue of being home-schooled are not being "socialized."
I agree that this is a general, and unfair criticism, assuming that homeschooling parents aren't the small minority who actually do prohibit their children from interacting with others. But in general children who are home-schooled are give the opportunities to interact with other children at the park, during sports lessons, for music or arts classes.
I do wonder whether home-schooled children are less likely to experience conflict with peers. Not bullying. Bullying is definitely a good thing, but being teased by friends can help introduce us to other perspectives, question our own, and hearing other's opinions can help us learn to accept, respond to, or ignore criticism. I think it is healthy to learn how to deal with embarrassment from peers. Being embarrassed intentionally by a parent is bullying. Being embarrassed unintentionally by a friend is a learning experience. Also, I think learning how it feels when you have offended a friend is quite valuable.
I can't remember the specifics, but I remember, in middle school, getting into a fight with my best friend over something I had said, flippantly. I remember thinking it would be just something in passing, but it really hurt her feelings, and we didn't talk for several days afterwards. I felt awful, and really came to understand why my comment was so hurtful to her.
Beyond this, however, organized school gave me the opportunity to routinely interact with people, in unstructured times (waiting before/after school, recess, and lunch), and learn how my world view wasn't the only one. There isn't the same amount of unstructured time to do that at sports practice, music lessons, or art lessons.
In general, think that there is a difference between spending an hour with children who are not your siblings, and spending a day with many child who are not your siblings. And I see a benefit in this. But, perhaps a very active parent can ensure their child will have several such opportunities, so this isn't, necessarily, a difference between home-schooled and organized-schooled children.
Complaint about organized schooling: Exploration and free thought
The people I know who are considering homeschooling are educated women. I have no doubts that they would find ways to ensure their children learned the appropriate materials, but, in my opinion, there are no benefits of homeschooling that cannot be achieved by an involved parent of an organized schooled child.
What especially gets me is the implication that children who attend organized school, do not get to experience the "wonders" of exploring the environment, or going on grand adventures. Phooey.
Heck, two days ago I was talking to a friend who worked it out so that both he and his wife had sabbatical at the same time, and they took their two kids to spend 2 months in France. They switched off their time, between research and homeschooling for those two months. What an experience! And then, when they returned to the US, they enrolled their kids in school again.
Maybe we can't all afford to do this, but neither can homeschoolers. However, we all can take our children on mini-adventures, either for an afternoon, a day, or a couple weeks, as time allows. Being in school doesn't prevent this. Having a disengaged parent does.