What is the difference between writing objectively and subjectively? How can someone write objectively about their own work (such as poetry)?

If you want to know the difference between writing objectively and subjectively, check the words in your dictionary and thesaurus. If you do the work yourself, you will retain it better than if I do your work for you.

As to the rest of your question, why would you as a writer want to write objectively, especially poetry? If you are a writer, you live in the product, especially poetry.

If you are so afraid of writing from your heart and soul and worried about what people think that you want to a sterile product, close your computer. Your aren’t ready to be out in the world.