These parents are raising their children in an environment where their convictions drive the education. Conviction leads to passion; it leads to direction; it leads to a sense of purpose. As a result, parents who homeschool out of conviction tend to be very successful teachers.
Think back to your favorite teacher. Was he an individual who did not really care about what he was teaching? Was she someone who lacked any kind of drive or purpose? I would venture to say that your best teacher was someone whose passion was evident. And when passion drives you, you can implement that passion into every subject, into every activity, into every aspect of your homeschooling program.
This is a huge advantage for homeschooling families. Not only do they have the opportunity to train their children in the way they should go, but their passion makes the program all the more dynamic. And this is a major advantage in any school setting.