Writing things by hand can just help facilitate that because it removes the ability to run the program and get the final result.

People can lean on their tools to 'guess and check' their work. Write a loop, run the program, and get an out of bounds error. They'll have learned oh this error means I need to subtract one from my loop bounds. And sometimes that works, though many times, it means there's an edge case they didn't properly handle.

When you only have pencil and paper and you need to explain to me what your code does you have to write down a representation of what's in memory and then how it changes step by step as the code runs.