I want to kill Paarthurnax because I like the Blades. All my friends didn't kill him so I want to find out, on my own, what it's like to.
I already killed Alduin and talked to the Blades. Now, they still want me to kill Paarthurnax and I agreed to kill him. So I go back to the Throat of the World where he is at and tell him they want me to kill him. He goes on about trust and what not and I attack him with my sword. He stays still like nothing happened. So I continue to attack him but then he flies up, lands and somehow he gets all of his health back.
Is this a glitch or am I missing something? If it is a glitch, is there any way to fix it?
For reference, I'm playing on Xbox 360.