Here's why:
* Poem: A piece of creative writing, often with a specific structure and rhythm.
* Poet: The person who creates poems.
* Letter: A piece of written communication, often personal and directed to a specific recipient.
* Writer: The person who creates letters (or any other form of written communication).
The analogy highlights the relationship between the creative work and the creator. Just as a poet writes poems, a writer crafts letters.