Emilia Clarke:Daenerys doesn’t know what she’s gonna do with him and the conversation that’s gonna be had. But then, before they can get anywhere, he shows her [the greyscale]. And I think that cuts to the core of the matter, which is that she loves him.
Dany had only meant their rooms in Illyrio’s estate, no true home surely, though all they had, but her brother did not want to hear that. There was no home there for him. Even the big house with the red door had not been home for him.