I have a houseful of gifted learners. Gifted learners require a completely different kind of education. Not just more homework, but a whole different approach to school. I put details on my Learning Lynx Classroom site here: https://sites.google.com/site/learninglynxclassroom/home/how-is-this-different-from-other-curricula.
Public schools are capable of doing this. Public school teachers, on the whole, seem to relish the gifted learning times. But public schools' mandate is too big, and they cannot possibly do what the law requires in giving an appropriate education to every child. The schools have opted to give their time, resources, and attention to the average and below-average children. They pretty much ignore the gifted kids because the gifted kids kinda do okay, even if they're being completely slighted and ignored. At least they're not getting Fs, right?
Some schools pay lip service to handling gifted kids, mostly in the form of extra homework (which isn't great). Some schools have gifted and talented programs, which do really really well with the moderately and even sometimes exceptionally gifted, but usually fail to help the profoundly gifted. Some schools are really good at adapting to gifted kids. Most of the teachers, administrators, and school psychologists I've interacted with want to help the gifted kids. It's not that the schools don't care. It's that they don't have the ability to help everyone, even if the law says they must.
This mom expresses the whole thing well: http://schoolsofthought.blogs.cnn.com/2012/08/23/my-view-the-joys-and-challenges-of-raising-a-gifted-child/ As she says, in many ways, gifted kids are special needs kids, but the schools aren't equipped to deal with their particular special needs, and often reject the very idea such smart kids even CAN be special needs kids--especially the 2e kids (twice exceptional) like Caleb and Benji.
So instead of doing the constant advocating for my gifted kids (advocating for one child times six), instead of fighting with teachers to get the kids appropriate education, instead of always searching for that one teacher in each grade who understands the gifted kids, I opted to do the work of educating them at home. It was easier for me, since I dislike conflict intensely.
I also wanted to avoid teaching the kids that they're valuable because they're smart, and only because they're smart. My kids, surrounded all the time by their equally-smart but differently-talented siblings, parents, and cousins, are not being taught what I learned in school: that being smart makes you better than everyone else. Being smart is just part of life around here, and it doesn't make you any specialler than any other talent makes people special.
Also, I really wanted to avoid teaching my kids what smart kids usually learn from the school system: that being smart is usually enough to get accolades, and work is unnecessary. And further, that if something is hard or you don't succeed the first time, you should absolutely quit and never try that again.
I don't want my kids to get big heads, or think other people are "less," or to be lazy and unwilling to take risks. And that's what gifted kids too often learn in public schools.
So we homeschool.