So is architecting, testing, validating, and even occasionally using.
This isn't the first time I've seen this phrase recently, but I'm not sure what the thought is a cliche or what it is intended to convey (don't read my note as negative, I sincerely am unsure what connotation folks are trying to say).
The idea behind "writing is thinking" is that people often overestimate their understanding until pressed to express it in words (or code).
How many times in your career did you sit down to tackle a task thinking you knew exactly how to approach it only to realize during implementation that there were edge cases you hadn't considered, API contracts that were now broken, or that the feature was trying to solve the wrong problem.
Having to be the one at the helm during implementation made you intimately aware of not only the problem at hand, but the current state of the codebase. That's something you can't replace with automation. You can't compress all of that context into your brain in a handful of prompts with Claude.
Remember the words of your math teacher--
"Watching someone else solve the problem doesn't mean you can now solve it too."