I understand why people homeschool their kids. However, the vast majority of students in this country attend public schools, and public schools are far from perfect. This means that most of the people entering the workforce are going to be coming from a background of public education. Seeing the problems with the system, parents might opt to remove their children from the system entirely. Great for the kid, but he or she is still going to enter an adult world full of public school graduates.
Whether you home school your kids or not, public education is funded with your tax dollars. What that means, most importantly, is that you have a say in how public schools are run. If you really believe that the public system is so bad and ineffective, your withdrawl from that system is an endorsement of that system. It's a simple civics lesson. If you have a say, but don't say anything, you have effectively endorsed the status quo.
So to answer the question...homeschooling is probably a good move if you want your child to have an immersive, engaging education that allows much room for critical thought. Another way to achieve that is to establish a public school curriculum that is immersive, engaging, and conducive to critical thought, and then send your child to public school.
Either way your child ends up fine, but the latter option creates a better world, one in which your child will find both like minds and numerous applications for his or her skills. But that's the whole point of state funded education in the first place. An educated public is a productive public, a public in control of its own fate. If we think it's failing (or if any of our government systems are failing, for that matter), we should, as citizens, act to make it right. "Public" education means the schools belong to us.