In my opinion, Holmes claiming he is the devil is a representation of how sick and demented he is as a human being. Throughout the book, Holmes showed little to no remorse for his victims. Instead, he felt a rush of sexual desire listening to their screams of fear and desperation. Holmes claiming he was the Devil is an accurate assumption and representation of who he really is.
Personally, I feel humans are inherently evil, but there is a small window with nurture where parents or guardians can alter the personality of the child for the better. In Psychology, you learn about the Nature Vs Nurture argument.