That's a polite denial - and in some cultures that is the proper response. Just like how some cultures require things to be asked three times. Once because it

That's a polite denial - and in some cultures that is the proper response. Just like how some cultures require things to be asked three times. Once because it is polite to ask - the other person, if polite, is expected to refuse. Twice because it is considered polite to ask again. Only to be denied again out of politeness. The third offer is the first "real" offer at which point the recipient can accept without being rude. A conversation might go like this: "Would you like to stay for dinner?" - "Thank you, but I wouldn't want to intrude." - "I insist! If you are hungry, please stay." - "Thank you, but I'm fine." - "There is enough food to go around - are you sure you don't want to stay and eat?" - "I will, thank you. / I'm not feeling hungry, but thank you." It's really quite silly. Many cultures cut it down to only having to ask twice with the first time being the expected denial and the second time expecting an honest answer.