A poem is a way to explain yourself. To decide how you want your story told. The more intimate you make it, the more you bare your soul. Which is cathartic. 

The surprising thing though is that the more you edit and make it more intimate, the more you get make a mystery of the facts.  It also immerses the reader in the poem so that they are not thinking about the circumstances of why the poem got written.

You get the catharsis, and the reader sees that they are not alone and gets to connect with humanity.