You've actually outwitted me zippitippitoes
I can't think how to explain this to someone for who it's not obvious.
I'll try, but rather expect to fail.
Take two sets of kids. One you give MMR to, the other you don't. If MMR causes autism you'd expect more of those who had MMR to get it more often.
Of course there is always a slight chance that even with carefully making sure the two sets are similar, random chance gives a false result.
So you need a good large sample to make this very unlikely. Since MMR has been given to millions of kids we do indeed have these numbers.
What's probably confusing you is that we don't have two separate groups. We have a time series where the number of kids getting MMR is varied over time.
If you vary MMR use up, then there should be an increase in Autism.
We do indeed see this, which fooled the arts graduates in the media and many ignorant mothers.
But a problem with time series is that if you sample kids over time they aren't easily comparable. New additives appear in food, expectant mothers are exposed to different chemicals and other environmental dangers.
But you can decrease the number of kids who get MMR, and see what happens to the autism numbers.
They have continued to go up.
This is not consistent with the idea that MMR causes Autism.
If it caused Autism, then the numbers should really have gone down.
They didn't. They went up.
Up is the wrong direction for a causal reduction in the input.
Of course being a right brained scientifically trained male, I believe in cause and effect, you may choose not to.
Although I don't believe it myself, the fact that Austism and MMR numbers have what we call a negative correlation, implies that it is possible that in a small number of children MMR actually prevents it.
The numbers are too noisy to really support the notion that MMR might be a preventative for austism, and the negative correlation varies by country for no obvious reason. But when something looks more like a treatment than a cause you have no good reason for thinking it is at fault.