look, i was homeschooled for 10 fuckin years. and from my personal experience and seeing the experiances of others, it works fine.
First off, SAT and ACT scores of students are on average higher than those of Public schooled kids, and kids not only learn the material but HOW to learn. One thing i've seen since going to public school is that kids learn to memorize shit and spit it back out on a test but not actually learn WHY something is the way it is, especially in mathematics.
Also, if you think that Homeschooling Parents just bullshit stuff, most if not all states require that homeschooled children take an annual test to show that they are in fact learning something. Ironically i used to take the California Achievement Test.
One more huge myth is that it makes children socially awkward and shit... NOT TRUE. They only become awkward if you shelter them.