Forgive me being blunt, but your topic title was not clear on what you are trying to get at, and then your message content was about Neanderthals and a youtube link to a television show. All of which are unrelated to your question. It makes it very hard to track what you are getting at.
Not everyone wants to cure "a species issue." A lot of people misunderstand Autism to be a curable disease, and because Autism is inconvenient to NT living, because of the attention requirements Autistics have (especially when younger), NT's want to "cure" it. Few people actually bother to research enough to find out that it isn't a disease, or an illness, it is a condition, a disorder you are born with (and which is hereditary).
Some NT's DO read up on this and want to STILL cure it by researching ways to prevent people from being born Autistic...to remove the Autistic gene in utero. Some famous agencies (Autism Speaks) seem to be accused of doing this.
But none of that explains WHY, which is your question. WHY do people want to cure it? Because it is inconvenient, as I said. Many (but not all) NT people are upset by Autistic life, and fear that it means the person who is autistic is automatically some sort of freak. The fear is variable...some people are afraid of different things, but the fear is the same.
Then some idiot decided that it was something that could be caused by vaccinations, which is a stupid claim, further stigmatizing Autism and making it all worse. Again, this is fueled by fear, and it causes more fear. Now some NT people are afraid that they might catch Autism, or their "perfectly normal" kid might catch the autism by being vaccinated. All of this right before a Pandemic, and it is pretty horrible seeing the results: Parents not vaccinating their kids, coming up with ridiculous excuses, and perpetuating lies to try to prevent something that isn't preventable. If a person is Autistic, they were born with it.
So that is your answer: Fear. People are afraid of things that they do not understand. And Autism is a very hard thing to understand. Plus it looks scary to other people when your kid is having a breakdown for no apparent reason. They tend to overlook the part where the kid is scared too, and can't really explain why.