The Blades are punks. Paarthurnax's help was integral to defeating Alduin, whereas they really didn't do a whole lot. He doesn't deserve to die.
You should kill him, but not for the blades' stupid reasoning. Who cares if he killed some Nords ages ago? What really matters is that Paarthurnax the most dangerous and powerful dragon next to Alduin. Letting Paarthurnax live is too risky.
Two things. One, Paarthurnax is powerful, but he is not immediately dangerous unless he has a change of heart. He will never be even comparable to the threat Alduin poses. Alduin is the World Eater. It's his destiny to bring about the end times. Second, by that logic we should be killing everyone that's not a peasant. Everyone with an abundance of power has the potential to abuse it and bring about terrible things.
Edit:
Since Bethesda just had to set up opposing factions for this one and force you to pick sides - your character should be choosing sides sooner, and the questline should have diverged, with your player approaching the same ultimate goal from different angles. The way it was handled was ludicrous - with the Greybeards on one side saying do what we say or we don't play....wait, it's our duty to teach you even though we strongly suspect you're gonna bump off our leader because we didn't properly indoctrinate you, and the blades saying kill Parthanaax to avenge our long-dead brothers we don't know or we won't talk to you. I'd like to know what the writer was smoking.

I agree with this. Didn't feel much emotional pull between the two sides. When the time to pick sides came, I felt like the Blades were just damn idiots, their moral ground was not strong enough from any angle. It really just felt like one way was good, the other was bad/wrong, rather than feeling like both sides had good and bad points.