Other people have covered this subject far better than I could. For instance, Bright Hub Education gives a summary of the pros and cons of being labeled with a learning disability:
Pros - IEPs, extra learning support, and specialized instruction
Cons - low self esteem, low expectations, and peer issues
At the end of the Bright Hub Education summary, the author gives a few ideas of what can be done to lessen the cons of being labeled:
Teachers can help prevent the negative consequences of the label by taking a few proactive steps to minimize the chance of problems occurring. Counselors and teachers should talk with learning disabled students and their parents and explain that a learning disability does not take away a student's value, that each person learns at a different pace and in a different manner and the school intends to provide the specialized education required to help the student achieve success. Parents and teachers should also be careful not to lower their expectations for the student and instead offer positive encouragement. Finally, teachers should talk to the class about learning disabilities and how different paces and styles of instruction are used. Open classroom discussions about learning disabilities can help to create an understanding between peers.
Those sound like laudable ways to address the problems, but I don't think they are as generally effective as educators and parents hope they will be. How can parents and teachers not lower expectations when they're being told that a child is not as able at learning as his/her classmates? And positive encouragement can backfire when used with children who are insecure about their abilities. Anti-bullying programs are associated with a increased rate of bullying, which makes it questionable whether open class discussions about learning disabilities will decrease bullying of those with learning disabilities. Schools may "intend" to provide "the specialized education required to help the student achieve success" but might fail at actually doing so due to lack of qualified personnel and resources.
Given that homeschooling helps a parent address both low self esteem (no classmates to compare one's self with) and peer issue worries, I can see why many parents choose to homeschool children with learning disabilities. At home, they can provide individual educations and extra learning support to their children, and they can independently seek out the specialists that their children need. It's a lot of work (and money to pay for the specialists), and I'm impressed by their efforts on behalf of their children.