I see some real potential problems with homeschooling but they are all a result of poor execution. There's always a chance someone isn't going to do a good job of something.

Mostly I hear that the children will miss out on developing social skills. That's up to the parents to make sure that their children learn manners and how to behave in social situations. If they were smart about it they would also make sure the children spend time with other children and aren't completely isolated from human contact outside of their family.

The other thing is to make sure they actually learn something valuable. As much as many people don't like it, mathematics is a part of our society. Language, writing and speaking is important as well. If you raise illiterate children that can't perform the simplest math problem, they are probably going to have a difficult time even if they stay isolated from society.

Many of the things children learn in public school have value. I just wish our government wasn't training the children to be good, obedient drones at the same time. I wish they would stick to education. The propaganda and social engineering can go away.

Even if the parents don't do the best job educating their child. At the end of it all that child will probably be a better human being than if they went through the government system. The government system trains obedient tax payers. It doesn't care about making decent human beings.