​Rhetorical device of pretending to refuse.

The oh-you-shouldnt-have figure.

Pretend disinterest, while actually desiring it. (akkismos affectation).

Accismus is showing disinterest in something while secretly wanting it. It's a form of irony where one pretends indifference and refuses something while actually wanting it.

In Aesop's fable, the fox pretends he doesn't care for the grapes. Caesar, in Shakespeare's Julius Caesar, is reported as not accepting the crown.

the accismus -- a fake refusal -- makes you look like less of a jerk than you really are.