Education Secretary John King says that homeschoolers are missing out on the rapid instruction public schools offer unless their parents are very "intentional" about providing it.
First off, what is "rapid instruction?" It sounds to me like the teacher presents concepts at a good pace. If you don't get material the first time, well, that's too stinking bad because the class has moved on.
If that's the case, YES, homeschoolers miss out on "rapid instruction."
If by "rapid instruction," he means that students learn concepts as quickly as possible and move on, then YES, often homeschoolers miss out on "rapid instruction." Many homeschooling parents will incorporate what they learned in other areas of life (adding fractions for baking and so on) and instead of learning the material and hopping to the next concept, it's implemented in the real world. That can make for a slower pace.
I'll add here that many if not most also miss out on doing most of their instructional time with computers, laptops, ebooks and the like. Computer-based instruction is often "rapid" and moves on when the algorithm thinks the kids "get" it. But parents aren't algorithms. They're involved start to finish with what their children are learning. I mean, unless they're "intentional" about not being hands-on.
I think it's interesting that this guy is all concerned about homeschoolers when only a third of public school eighth-graders read proficiently and a fifth don't graduate at all! I think his real "concern" is the power his department loses when people unhook from the public school system.
Perhaps a better way to deal with homeschooling from his vantage point would be to make public schools so wonderful that no one even considers leaving.