Poetry is so different from any other kind of writing. There are no "rules," really, and you get to form and shape your ideas any way you wish without worrying about the conventions of writing, such as punctuation, capitalization, and complete sentences. Poetry offers an opportunity to express what you're feeling in a way no one else could, and frankly it allows you to say things which need to be said (both awful and amazing) without everyone necessarily knowing all the details. You can tell how it feels or how it looks to you without telling all. Conversely, you can take the tiniest observation and give it a full and detailed expression in poetic form. There are certainly forms and conventions for poetry; however, at its core, poetry is a form of expression which allows you to do whatever you want, however you want, as long as you're expressing yourself.
In his "A Poet's Advice," e.e.cummings declares that a poet is somebody who feels, and who expresses his feeling through words. Poetry, he contends, is feeling--not knowing or thinking. To express one's feelings, one must use fresh, innovative expression, not the words of anyone else. Such a task is not easy. Cummings suggests that young people do something easier, unless they are willing, even glad, to feel and work and fight until you die.
Writing poetry is like composing music or drawing and painting: it is original expression of a person's feelings using words unique to that person's feelings. To know that one is truly alive is to write poetry.
I think you could pose this question as: "Why practice any hobby that isn't necessary for sustaining life?"
I think you should write poetry if you love it. Write because it makes you feel good. Write because someone you love wants to read it. Truly, when it comes to art, I think you should only do it if it brings you or someone else pleasure. Generally speaking, art does not equal money - so don't do it to make a living. If you happen to make a living doing it, that is great. But do it because you love it.
This will get many responses. I think that the fundamental reason why poems are written comes from a need to express something. I will try to veer from the typical depiction of the poet as one who is emotional, but it is really difficult to divorce the subjective experience from the poetic expression. There is something that is clamoring to be said, expressed, conveyed in a poem. It is venue that praises and lauds this experience and its articulation. Whereas the novel might have different conventions attached to it, the poem is one where subjective experience seems to be a dominant convention. If I could offer one other element to why write poems, I would say that it helps to fulfill a cliched state of being. I listened to a professor describe what his youth was like: "So, here I was- this angry youth, with my black jacket collar hiked up high, and a copy of Byron in my pocket near a flask of scotch and I felt really good about myself. I was angry and didn't care who knew it." Somehow, this image stuck in my mind with the question. The comedian Henry Rollins describes the same experience when he suffered a break up and how poetry (and Miles Davis) was therapeutic. (Humor not withstanding.) There are times when poetry helps us deal with the challenging times because it allows us to absorb ourselves in our own experience. If the subjective is something that is critical to the exploration of poetry, then to be able to revel in it as a poet means that we are able to revel in ourselves, indulge in narcissistic behavior without the fear of being labeled as a "narcissist." Instead, we can be called a "poet." This might be a bit on the sardonic side, but I think there is a shred of truth to it.
It is on of the purest forms of written expression. You take every way in which we write, and every thing we put in our writing, and we boil away the extras down to the core, basic and specific words. Then we arrange them for maximum effect and structure.
It is also a writing style that allows us to be artistic - to arrange the words as lyrics without music, and the stanzas so that, when read, they impact the reader in a specific way that we intend.
In doing this, I find that I also tend to express thoughts, feelings, beliefs and observations that I wouldn't normally talk or write about. Poetry encourages us to be as honest as possible (it takes more words to lie), both with ourselves and our readers. So in poetry, I often find courage.