The Elder Scrolls V: Skyrim's most heartbreaking quest asks the Dragonborn to kill Paarthurax at the request of the Blades. However, the Blades do not ask them to kill Odahviing, Durnehviir, or other warmongering dragons to prove their loyalty to the organization. This suggests Paarthurnax's bounty stems from the Blades' desperation to control the Dragonborn and separate them from the Greybeards.
Long-time fans of The Elder Scrolls franchise likely recognized the Blades, an ancient organization first appearing in Morrowind. Also called the Imperial Intelligence Service, the Blades were sworn defenders of the Dragonborn Emperors and dedicated worshippers of Talos. When the Septim line died out, the Blades remained in service to the Tamrielic Empire but continued searching for the next Dragonborn. The Blades thrived under Tiber Septim, who was not only a Dragonborn but a warmongering leader. Desperate to return the Blades to power, Esbern and Delphine require Skyrim's Dragonborn to prove their loyalty time and time again, leading to the eventual demand for Paarthurnax's death.
Shortly after Skyrim's White-Gold Concordat was signed, the Empire disbanded the Blades organization. Many Blades died in The Great War, and more perished after the Empire's defeat. Delphine and Esbern, Skyrim's Blades, believe they may be the last members left. While the Blades consistently encourage the Dragonborn's homicidal tendencies, the Greybeards promote a life of pacifism. This lifestyle directly threatens the Dragonborn's relationship with the Blades, who thrive on the conquests of Dragonborn leaders. Delphine is thus encouraged to terminate the relationship between the Dragonborn and the Greybeards by ordering Paarthurnax's death.
Skyrim's Blades Intend To Separate The Greybeards And The Dragonborn
Delphine's justification for demanding Paarthurnax's death is due to his past service to Alduin. During Skyrim's Dragon War, Paarthurnax served as one of Alduin's lieutenants. He claims to have seen (and committed) unspeakable acts against humanity. However, shortly after Alduin's false claim of godhood, Paarthurnax defected and taught mankind how to use their Thu'um. He has since remained isolated, meditating on the Way of the Voice and distancing himself from temptations. As the master of the Greybeards, the organization is protective of Paarthurnax, hiding his identity from the Dragonborn until they prove themselves.
When Skyrim's Dragonborn receives the quest to kill Paarthurnax, they may question Delphine about her reasoning. She states that due to Paarthurnax's past and betrayal of Alduin, he is untrustworthy and poses an immense risk to mankind. This reasoning fails to explain why she doesn't order Odahviing and Durnehviir's deaths as well. Odahviing must be defeated in combat before he serves the Dragonborn, and refuses to assist in defeating Alduin. His more recent betrayal and limited assistance should make him more suspicious than Paarthurnax, but Delphine fails to comment. Similarly, Durnehviir is a dragon warlord who conspired with the Ideal Masters to obtain an undead army. Durnehviir never renounces his warmongering ways and is a much greater threat than Paarthurnax. Still, the Blades do not order his execution. Odahviing and Durnehviir's pardons are proof that losing influence over the Dragonborn is far more threatening to The Elder Scrolls' Blades than dragons.
In The Elder Scrolls V: Skyrim, the Blades fail to present any convincing argument for Paarthurnax's death, seeking to control the Dragonborn and cut them off from organizations that would temper their powers. Paarthurnax admits he may succumb to his urges one day, but this does not warrant his death. His rehabilitation and the Greybeards' companionship to the Dragonborn could prevent a greater calamity the Blades' violent urges may invite.