He's not gonna throw grown man bars. Push wants to play in the mud. Drake CAN'T play in the mud and retain the same image he had beforehand. Budden said it best. He's forced Drake to compete against his integrity.
Do I win this battle with Push and take it to the sewers? Or do I lose the battle with Push and keep my relatively clean, wholesome image?
Which one is more important to him? He can't do both.
Rap came from the dirt and is/can be dirty as fuck. Drake is the antithesis of that and that's largely responsible for his success. What will his legion of Stans think of him if he goes that route though?
And Pusha has made it clear that he can/wants to play this game for awhile. How much time can Drake afford to spend on this? What's he willing to sacrifice if he knows he could still end up on the losing side?