Here's the canonical example: A is correlated to C. B is correlated to C. A is NOT correlated to B. How is that possible? The argument is that, if causation

Here's the canonical example: A is correlated to C. B is correlated to C. A is NOT correlated to B. How is that possible? The argument is that, if causation is unidirectional and acyclical, then the only causal structure that leads to the above is that A and B both cause C. There's no other way to do it. And you can derive causation from observational data! Of course in real life there are a bunch of problems with this, particularly measurement error and hidden unmeasured or unmeasurable variables. But more or less those exist with experimental data as well. You can only conclude things about observed variables and a very large number of unmeasured variables could throw off your inference. Anyway, I more or less held your belief on this until I read Pearl's (and colleagues') material. There's much more expansion to it than the canonical example above.