It all began with just one individual, Andrew Wakefield. Wakefield published a paper in 1998 which claimed there was a link between the Measles, Mumps, and Rubella (MMR) vaccine and autism.
Before investigators found he was being paid by entities profiting from destroying the vaccine industry, the public ran with the story.
Meanwhile, researchers were unable to reproduce his findings. His coauthors withdrew support of the article, he was found to have mistreated the developmentally delayed participants in his study, and the journal which published his paper retracted it completely before Wakefield was struck from the UK Medical Register and was barred from practicing medicine.
His work was called an "elaborate fraud" by the British Medical Journal.
Subsequent reporting by Deer revealed that Wakefield had planned to capitalize on the MMR vaccination scare provoked by his paper by forming a corporation that would profit from "litigation-driven testing"
Despite this unanimous dismissal of Wakefield's findings, he was able to drum up a following among a small group in the general public to pass off his dismissal as a conspiracy against the truth. As a result, vaccine rates declined.
Stripped of his medical credentials, he continues to rally against vaccines today, supporting a movement that spreads deadly, preventable diseases.
Despite the case essentially being closed, study after study has come out showing once again there is absolutely no correlation, much less a causation between autism and vaccines.
As this graph shows, the unvaccinated participants in this study actually followed the trend line of autism (the lighter band) just as well as the vaccinated. If vaccines caused autism, we would see the dotted line well outside of the band of autism incidence.
...no increased risk for autism after MMR vaccination was consistently observed in subgroups of children defined according to sibling history of autism, autism risk factors (based on a disease risk score) or other childhood vaccinations, or during specified time periods after vaccination.
Why do people still believe vaccines cause autism?
There are well known psychological effects that lead reasonable people to hold to this claim. Some of this is simply a lack of exposure to data and an abundance of confirmation bias from followers of Wakefield.
Sometimes it's because parents end up in difficult situations and having an enemy can ease the pain. For this reason, antivaxx groups are known to target parents who have children born with autism or tragically lose their infant children due to rare diseases.