The main two themes of "With All Flags Flying" by Anne Tyler are pride and stubbornness. In the story, the old man is too stubborn to listen to the offers from others and is dead set on going to live in a nursing home.
The stubbornness that the old man exhibits is a byproduct of his pride. He is too proud to see himself become a burden to any of his daughters. For that reason, he is unwilling to concede on his plans to live in a nursing home. The man wants the ability to check himself into a nursing home willingly instead of being forced to go to one when he becomes a burden, which again relates back to his pride.