Board Thread:Lore Discussion/@comment-26213507-20150715194939/@comment-6881629-20150831150709

Balgruuf will not let you use Dragonsreach to trap Odahviing while the civil war is happening, as it would leave Whiterun open to a attack -

"Ulfric and General Tullius are both just waiting for me to make a wrong move. Do you think they will sit idle while a dragon is slaughtering my men and burning my city?"

So you have to at least temporarily stop the civil war for him to cooperate, Vignar Gray-Mane will also say something similar if he is Jarl and the civil war is still going.