It is very difficult to accurately explain what the purpose of poetry is. When asking: Why do we have poetry? There are a number of things to keep in mind. First, human cultures have been invested in artistic creation for thousands upon thousands of years. Much of the earliest evidence of human behavior that still survives today has to do with art, like cave paintings and small sculptures. It is likely that the reason that poetry exists is because creating it is irresistible for humans. On an individual basis, each poem is likely to have its own reason for existing.
