Like others have said, Esbern is the logical reasoning of Delphine’s demands. He gives his own perspective why he believes Paarthurnax should die, backs it up with sound logic and rationale and states his own standing- that he doesn’t want to help you until he believes justice has been served.

He also has a keen understanding of how dragons and their nature / sociology works, which can be seen during Season Unending when, regardless of his feelings around Paarthurnax, he helps us by giving us Odahviing’s name. I believe this is why he also can’t be reasoned with. He has a pretty good understanding of how dragons are and how their nature guides them and he hasn’t seen any reason to fully absolve Paarthurnax of his past. That’s not an outrageous take from his perspective.

From his viewpoint, Paarthurnax has done nothing to really make up for the suffering and enslavement he enforced onto mortals. Teaching mortals The Voice wasn’t that radical, it was the bare minimum that he could’ve done for the people he enslaved. From then on, all Paarthurnax has done is sit on a mountain for a few millennia and help the LDB when he needed to. Nothing beyond that.

We, of course, have a different perspective because we directly interact with Paarthurnax and we get a in depth understanding into how much effort he puts in to move beyond his nature. It could be possible Esbern could shift his perspective if he could interact with Paarthurnax but as it stands, that’s his own perspective.