I would say that most of the parents here are very "supportive" of homeschooling, it is suggested often, and agreed to be a solid option for those who can do it. Just because most of us don't see ourselves being able to do it does not mean we are not supportive of it, or aware that at times it may truly be the best for the child. But every child is different, and every family is different, and I believe in allowing parents to make the best choice for their unique family while having all the options laid out clearly on the table. While I think I would make a lousy teacher for my son, I continue to keep homeschooling at play in the back of my mind should the balancing act with the public school fall too far out of whack.
As for special schools, I'm not sure what you are thinking of there. Our county does have a special day class for autistic children, but it would be absolutely the wrong placement for my son, because these are all Kanner autistic children who have trouble with most aspects of daily living much less education. There is no allowance in that program for a bright child like mine; higher functioning kids are expected in this district to be mainstreamed and supported with an IEP. My son has dreams and goals, and will need a certain level of achievement in education to get there.
There is one wonderful special school here that is private. While most of the children are lower functioning, the design does allow for a higher functioning child to advance at a quicker pace, and I've met some of those children. But this school is incredibly expensive, and as much I think it is a wonderful place, I haven't gotten the sense that it would be a better placement for my unique child, even if we could afford it (which we can't). There remains that balance between what he can and wants to achieve in school, and his needs related to AS.
In the end I guess it varies by what is available in one's area, what the unique child's issues are with school, and how the family as a whole is situated. I truly try to support all the options, and encourage parents to figure out what will work best for each unique situation. I think most parents here are the same. Basically, I think we "support" what each family chooses for themselves.
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Mom to an amazing young adult AS son, plus an also amazing non-AS daughter. Most likely part of the "Broader Autism Phenotype" (some traits).