A structured education is essential. Public schools do not provide much of that and have many problems besides, such as you mention, and in my experience private schooling is a mixed-bag. My concern would be (were I a parent) that it may be difficult to provide this when homeschooling. A tutor might help but then you'd better make sure to be on the same page and clearly delegate certain authority to the tutor.
RE: Why We Chose to Homeschool