oo there are quite a few reasons with many varients, ill try to list a few...
1. censorship - you could get into real trouble for writing poetry, esp if you were are a woman/ethnic/poor etc. no one wud publish you
2. you dnt want to associate the poem with ur identity. keep it a secret from ur true love or dnt want anyone to know ur a fascist etc.
3. people just write things to put it out there, they can be one offs, everyday sayings, motos, philosophys, thoughts, diary entries, hymns etc.
4. we dont actually no hu wrote the poem lol
hope that helps