They don't.
I'm sorry. This is America, and people are allowed to have their opinions. But if you think vaccines cause autism, your opinion is wrong. I hate to be the person to say that, but even if there was a correlation between vaccinations and autism, would you rather your child have measles or autism? For me, I would rather live with autism than die a slow, painful death from these diseases that have been eradicated from our radar.
Could I give you an endless amount of statistics and facts from science? Yes, I could. But will I? No, I won't. Here's why: People who are stuck on an ideology that they find threatening will not listen to statistics and big words. Instead, I will give you an example behind the dangers of anti-vaxxing. I could give countless statistics and facts from the CDC, but that won't be enough.
A 5-year-old French boy recently traveled to Costa Rica with his family. This same boy had not been vaccinated by his parents, and when he entered Costa Rica, he was exposed to the measles virus and flared an outbreak. This outbreak is a danger to those who have not been vaccinated and even those who are vaccinated.
Vaccinations are disease prevention, not a cure.
I think that people forget that the goal of vaccination is to eradicate diseases by building the immunity of a community. When this immunity is broken, the chances for death are at an all-time high.
Do you want to be this person? The person who ends up in the news because they refused to vaccinate their child due to a fear of a fable created by society? If you still find yourself leaning between one or two, think of this situation: Would you rather have an autistic child or a dead child? That is the reality of anti-vaxxing. It's a decision between your child's mortality and the mortality of those around you.