In layman's terms, David just wants to make mistakes. He knew that Walter knew that the poem was written by Shelley instead of Byron, but he insisted. One of the important reasons is to let Walter choose to stand aside through this lie. The inner monologue is to tell Walter that I made a mistake on purpose. Do you want to admit that you agree with me (kiss my ass) and stand on my side to fight against mankind with me?
If you expose me, you'll have to part ways with me. So the ending is clear to us. Walter exposed David.