Spoilers on the main quest:
When the Dragonborn captures Odahviihg, he learns that Alduin's portal to Sovngarde is on Skuldafn, on the Jeroll Mountains on the far east of Skyrim. Wouldn't it be more wise to keep a untrusted dragon captured and go to Skuldafn with a dragon he already trusts ?
I don't know if It's possible, or if Paarthurnax tells the dragonborn why he doesn't or can't bring him to Skuldafn, does someone has any information about this or a lore-reason for this ?