While I can see a number of significant advantages, I have (probably unfairly) developed a bit of a prejudice against homeschooling. A college friend of mine was homeschooled the whole time, and it was more difficult for him when he started college. His math skills were not up to par and the things we all took for granted since we'd done it for so long were unnatural to him.
I also worry about the social side of the coin.
Much of our adult behavior is molded by our childhood experiences.
No matter how many homeschooled kids programs you participate in, they seldom get the expereince of working in a group environment, which can make it more difficult when they have to move on to those situations as a young adult (most jobs - particularly entry level, are cooperative environments). They never learn to work with difficult people or people they don't like - another part of the real world. Having a unpleasant teacher isn't that different from having an unpleasant boss - how does the homeschooled kid learn to deal with that? It seems so sheltering to me.
there is so much they miss out on - both good and bad, all of which helps develop your personality..
I'm sure some parents ARE able to compensate and give their children all the experiences they need. But I know I would not be up to the task.