Well, for one, it's not a disease; it's a developmental disability (and some of the milder cases, you can make an argument for it not even being a disability). Autism is atypical development, not a dysfunction of some pre-existing order. Just like you couldn't say that someone with dyslexia or a learning disability has a "disease", you couldn't say it about autism.
Second reason: Autism, by its nature, changes the way you learn and the way you process information. That changes your life and your experiences of the world to a great degree--and it affects your personality, too. Autism is part of the way the brain works, and to the extent that the self is the arrangement of connections in the brain, autism is part of the self. People who accept themselves for who they are tend to also be proud of the autism, deficits and all, because it is part of their identity.
Third: Autistic culture. Research Deaf culture; they've been doing it for ages longer than we have, ever since they got themselves a common language (group of languages, actually) and gathered in one place to talk things out. Autistics got that when the Internet and computer technology became available. Once the first few autistics connected via the Internet, we started forming our own way of communication and interaction. Autistic culture isn't limited to those who can speak, which is where technology comes in: When speech is undependable or absent, anyone who can pick out letters or symbols on a modern communication device can connect to the Internet and communicate with other autistic people. That wasn't possible before digital computers. Now we have not just autistic people, but those in the broader autism phenotype (people with autistic traits but no disability), and parents, spouses, and significant others of autistic people.
Fourth: Disabled people have the same problems that any minority has: Marginalization, prejudice, stereotyping, lack of communication, lack of acceptance. The disability rights movement includes plenty of people who say that part of their identity is their disability; and among those people are autistics. Being a part of a minority affects how you live; so it affects your identity. Many disabled people are proud of being disabled for the same reason that black people might be proud of being black.
Last, a trivial but culturally important reason: Many autistic people have autism-related special skills, either savantlike or the result of years of practice thanks to a special interest. Being proud of your skills is practically a human universal; and even when autism includes deficits that overshadow your special skills, there's nothing that says you can't be proud of being able to do things that most other people can't. Disabled doesn't mean universally incapable, after all.
One last note: Cultural pride does not, and should not, mean a feeling of superiority. Autistic people are neither superior nor inferior, and elitism--even reversed--only leads to the very hatred and prejudice we're trying to fight.
Second reason: Autism, by its nature, changes the way you learn and the way you process information. That changes your life and your experiences of the world to a great degree--and it affects your personality, too. Autism is part of the way the brain works, and to the extent that the self is the arrangement of connections in the brain, autism is part of the self. People who accept themselves for who they are tend to also be proud of the autism, deficits and all, because it is part of their identity.
Third: Autistic culture. Research Deaf culture; they've been doing it for ages longer than we have, ever since they got themselves a common language (group of languages, actually) and gathered in one place to talk things out. Autistics got that when the Internet and computer technology became available. Once the first few autistics connected via the Internet, we started forming our own way of communication and interaction. Autistic culture isn't limited to those who can speak, which is where technology comes in: When speech is undependable or absent, anyone who can pick out letters or symbols on a modern communication device can connect to the Internet and communicate with other autistic people. That wasn't possible before digital computers. Now we have not just autistic people, but those in the broader autism phenotype (people with autistic traits but no disability), and parents, spouses, and significant others of autistic people.
Fourth: Disabled people have the same problems that any minority has: Marginalization, prejudice, stereotyping, lack of communication, lack of acceptance. The disability rights movement includes plenty of people who say that part of their identity is their disability; and among those people are autistics. Being a part of a minority affects how you live; so it affects your identity. Many disabled people are proud of being disabled for the same reason that black people might be proud of being black.
Last, a trivial but culturally important reason: Many autistic people have autism-related special skills, either savantlike or the result of years of practice thanks to a special interest. Being proud of your skills is practically a human universal; and even when autism includes deficits that overshadow your special skills, there's nothing that says you can't be proud of being able to do things that most other people can't. Disabled doesn't mean universally incapable, after all.
One last note: Cultural pride does not, and should not, mean a feeling of superiority. Autistic people are neither superior nor inferior, and elitism--even reversed--only leads to the very hatred and prejudice we're trying to fight.