The infographic below, taken from www.gratefulforgrace.com, shows the relatively better performance of homeschooled children as opposed to those attending “regular” school.
Without getting into a discussion of these numbers, my (strong) opinion is that even if they are true (meaning statistically significant once corrected for other variables), they are not “the whole story”.
Kids need socializing, mingling with peers, learning to cope with difficult people and be exposed to difficulties as this is the only way to learn overcoming them. Only “regular” school can provide this.
Also, for society as a whole, kids should be exposed to a wide range of ideas that they will evaluate on their own. Families do and will always play a major role in shaping the children’s attitudes and ideas especially in the early stages. Giving them a complete monopoly in developing the young minds (what happens with homeschooling) tends to reinforce the parents “radical” ideas (religious, political, philosophical etc.) with a risk of producing a “fanatic” of sort.