From my experience with homeschooling groups, a great majority of homeschoolers do so for religious reasons, e.g., ensure that they're not exposed to science teaching that contradicts young earth creationism, or sex education, etc.

Or just to prevent their children from being infected by "worldly values". You'll often hear them say "Be in the world, but not of the world."

There are of course, people who do it to give their children an education that they feel is superior to the regular one, but they are a minority.

Of course, I didn't survey all homeschoolers to come up with that, I suspect you'd find clusters of secular homeschoolers in certain areas on the west coast, but elsewhere, Jesus dominates.