I once had a dream that Alduin was female and got pregnant from Paarthunax. After the main quest Party sent me to destroy the eggs Alduin laid, but they already hatched and I kept them, breeding myself some dragons. Sounds like a fanfic.
This reminds me of the mini talk they have during Alduin's Bane Alduin: Join me, or perish with your mortal friends! Paarthurnax: No.... never again! Me: Okay, that alone made me feel more sad than it should have...
Well, not only was it to wait for Alduin, I also think it was to atone for his horrible actions during the Dragon Wars. And then the Blades want you to kill him...never mind the fact he was the first to teach humans how to use shouts, so he's the reason that everyone isn't dead or enslaved!
Well, if you go through the peace treaty, you'll be given the quest, even if you never return to Sky Haven. If you end the civil war, you can ask Paarthy for Odahviing's name. The first time they asked me, I shouted them off the mountain, stole all their stuff, then never came back.