Even speaking is thinking. This is why free speech is the very First Amendment. Whoever denies your right to speak freely is controlling your thinking.
Writing is thinking with a superpower. It's like using the "Pensive" from Harry Potter, depicted in the scene where Harry and Dumbledore pull memory whisps out of their temple to rewatch in a mirror pool. Writing enables you to apply your attention to an idea at multiple levels of analysis with significantly less effort than doing the same while also preserving the idea in your head manually.