How would you argue that a poem is the perfect form of expression?

In my opinion, poetry's main competition as a form of expression is prose.  

Because prose is your main competition, you are going to need to focus on the negatives of prose and focus on the positives of poetry.  With that said though, do not completely ignore the positive things that prose does.  If you begin your essay by saying that prose is horrible, you risk alienating your reader.  You do not wanta reader...

In my opinion, poetry's main competition as a form of expression is prose.  

Because prose is your main competition, you are going to need to focus on the negatives of prose and focus on the positives of poetry.  With that said though, do not completely ignore the positive things that prose does.  If you begin your essay by saying that prose is horrible, you risk alienating your reader.  You do not want a reader on the defensive.  Start with a thesis statement that admits the positives of prose while stating that poetry is superior.  For example: "Although prose is a solid form of expression, poetry is a far superior form of written expression."  

The above thesis is specific in its intent, but it is broad enough to allow the body of your essay to pick and choose aspects of prose and poetry while still supporting your thesis statement.    

While I do enjoy reading prose more than poetry, I will admit that poetry does certain things better.  Focus on poetry's ability to create vivid imagery in a relatively short amount of space.  Poetry is typically very image dense when compared with the number of words on a page.  Prose on the other hand often takes multiple pages to explain a similar image.  I would also focus on poetry's ability to create rhythm while incorporating rhyme.  Prose can be detailed for sure, but it just can't ever create that "sing song" feel.  If the goal of expression is to tap into an emotional core, poetry taps the core more quickly than prose. That's why people write poems and set them to music. They are called songs.  Nobody puts prose to music.  

I would also make sure that the positives that you choose to mention regarding prose are also positives that poetry can do as well, only better. Your job isn't to discredit prose.  Your job is to show poetry as superior.  Take character development for example. Prose is often praised for its ability to concretely develop a character in deep ways. Poetry is capable of doing that too.  In fact, that's what the dramatic monologue poem style is all about.  My favorite in that genre is Browning's "My Last Duchess." The character of the Duke is so well created in that poem.

For your conclusion, try to push your reader into further considering and exploring poetry as a superior form of expression.