I couldn't possibly
What it really means
A ritual first refusal of an offer — the last slice of cake, a favour, a gift. Tradition allows the other person to insist once or twice, after which accepting is perfectly polite.
Context, tips & common mistakes
"Oh, I couldn't possibly" refuses generosity — the last biscuit, a lift home, being paid back — and roughly half the time it is the opening move of a ritual rather than a decision. The full dance: offer, refusal, insistence ('go on, honestly'), acceptance ('well, if you're sure…'). The refusal preserves modesty; the insistence proves sincerity; everyone gets what they wanted.
Reading it: a ritual refusal is light, smiling, often already reaching; a real one repeats firmly with a reason ('honestly, I'm driving'). Respect the second refusal — pressing past it converts hospitality into pressure. Performing it: one round of 'oh no, I couldn't' before accepting the favour reads as beautifully mannered, and 'well, if you insist' is the approved surrender. Related species: 'you shouldn't have!' (delighted gift acceptance) and 'only if you're having one' (yes to tea).