Why can't I defeat Paarthurnax?

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.

Paarthunax is a strong dragon, but gaining health? That I dont know. But if he does, kill him as fast as you can, use powerful weapons. Use a melee weapon and get ready to pull out ranged destruction spells or a bow. After that youll be able to kill him. If it doesnt, get stronger and try again.