(Because I don't want to put my entire post in spoilers, I'm giving you a warning now. Spoilers lie ahead.)
So, Esbern and Delphine refuse to talk to me because I need to kill Paarthurnax. Do I really have to? I rather like Paarthurnax.
I simply refused to do it. Screw their useless order, it's as dead to the world as they are. Think about it, if Paarthunax's plan is to teach all dragons the way of the voice, then there would be absolutely no need for the blades. So, you are basically deciding, do you want to be part of a group of genocidal creeps or do you want to take a chance at saving all the dragons from their corruption by Alduin and not being shunned by Grey Beards. It's not worth it to do anything that beotch DEMANDS if you ask me. I thought it would have been poetic justice to call down my pet dragon to eat Delphine the Mad; but, alas she is essential and cannot be killed. LAME!