[Natsu]

Causation has a direction, but the equals sign doesn't, is probably an overly-pithy summary of the first section of the book. And it was hard to represent the simple observation that effects come after causes, not before.

So they introduce do calculus to intentionally break that symmetry to test causal models, which themselves are basically directed graphs going from cause to effect. These also help you see what you need to test to try to falsify your model and to show you how to measure how much of the variance in an effect is explained by variance in the cause. And it helps keep track of interventions, like opening doors in the Monty Hall problem[1].

There's a more detailed summary here that looks pretty good which probably does a better job than my quick summary. I skimmed it and it matches what I recall from the book:

https://www.tosummarise.com/book-summary-the-book-of-why-by-...

[1] https://en.wikipedia.org/wiki/Monty_Hall_problem