Our educational system has often generated mediocrity except for gifted athletes. From kindergarten, children are bombarded with pressures that urge them to modify their behavior and intellectual development toward the average of the group. Gifted children throughout our society may be trapped in an intellectual wasteland - a world that can be cruel to the gifted (Garfield, 1980).
-Webb, Meckstroth, and Tolan. "Guiding the Gifted Child: A Practical Source for Parents and Teachers."
I get very tired reading screeds against homeschooling because almost always, the person who is opposed to homeschooling ignores two very important things about public schools: (1) all except the most progressive public schools cannot or will not meet the educational needs of advanced children, and (2) the "socialization" that is present in public schools can be very harmful to the emotional well-being of gifted children.
If you bring up these points, the response to (1) is that gifted children will get along fine. They ignore the fact that gifted children will very often spend 50% of their time in school waiting for the other kids to catch up. They learn not to be challenged. The notion that children should always be with their same-age peers overrides the notion that these children have advanced intellectual needs and can feel like they're starving while waiting for something challenging.
The response to (2) is usually something that it is the gifted child who is "screwed up" and needs to learn to get along with other kids. It is completely ignored that school is the only place in the world where someone is forced to sit in a classroom with people of their same age but who may otherwise have nothing in common. It is also ignored that such a system is very intolerant of differences.
The emotional repercussions of such a system are horrible. Gifted children, at the very least, never learn how to put forth effort. When they finally do encounter a challenge (usually in college), they may have to deal with a lot of frustration. Some of this frustration can actually cause them to quit college. Never having been challenged can make them feel like they are stupid and can't cut it.
At the other end, you could have anger. In the book, "Misdiagnosis and Dual Diagnosis of Gifted Children," they discuss the prevalence of gifted students among students who have been the perpetrators of school shootings. These children are teased and harassed to the point of wanting to take other people's lives. Fortunately those that get this angry are relatively rare, but the consequences are, quite literally, deadly if the anger becomes too much.
What is most frustrating is that the people opposed to homeschooling do not provide alternatives for children with these needs. (They also ignore that some of these issues affect even non-gifted children.) They just say that the public school isn't perfect but it is certainly better than homeschooling. I wonder if they would feel any differently if it were their children going through these kinds of problems.
Carnival of Homeschooling