This was recently mentioned by a parent.
A high proportion of doctors were educated in independent fee paying schools. These schools generally don't accept children with disabilities of SEN, even if they are academically high ability. It has been known for children with ASD and Asperger syndrome to pass entrance exams for these schools with flying colours, but then get rejected at interview or end up being 'kicked out' in the first term for being weird or not fitting into the environment. This result of this is that such doctors do not have any classmates with ASD in school.
The parent thinks this goes some way to explaining why it's rare to find doctors with any real knowledge of ASD.