I think, more than anything, Benedict was just exhausted, and the exhaustion was taking its toll on him, so that he could no longer perform his duties at the level he wanted them to be performed.
Such a realization is a hard one to make, but it amounts to continuing to fight, and failing, until it kills him; or accepting that it would be best for all concerned that he step aside, that he can rest and be restored, and still contribute, but not at such a debilitating pace.
His words are no longer doctrinal, so they can be conversational. Gentle, learned advice for Pope Francis in private, with no axes to grind, or palace intrigues to consider.
I know what you mean, but for the casual reader let me pick a nit: Popes, like everyone else, can have light conversations, joke, fool around, err doctrinally, and generally be human as they are. The Pope is only infallible when he speaks solemnly, indicates that he proclaims the eternal faith of the Church, in his capacity as the head of the Church, and concerns faith and morals.