More information here: https://en.wikipedia.org/wiki/Code_refactoring
There are many goals in refactoring, specifically this section:
> Potential advantages of refactoring may include improved code readability and reduced complexity; these can improve the source code's maintainability and create a simpler, cleaner, or more expressive internal architecture or object model to improve extensibility. Another potential goal for refactoring is improved performance; software engineers face an ongoing challenge to write programs that perform faster or use less memory.
I was addressing OP's analogy to cutting pieces of written prose and rearranging.
Code is meant to be read by humans and only incidentally by computers.
A lot of architecture is just being clear about what is intrinsic complexity and what is accidental, be it cognitive or computational.
you are either using a different definition of architecture or this is wrong. Refactoring is bottom up construction. Most of the time when I see people frustrated or struggling (including myself) it's because they have forgotten this and need to take a break.