The Thai was a little bit put out because he perceived the matter as Andy declining his hospitality. Andy was also a little irritated because he thought that the Thai might not have understood what Andy had said in English. Behind the scenes was another story. When Andy said that he was fine and didn't want anything, the Thai had perfectly understood Andy's English. But in Thai culture , reading between the lines, this scenario would be seen quite differently from simply an offer of a drink and a courteous refusal.
Thai answers are often more subtle than English ones.
In our Buddhist society, every morning, the monks walk slowly past people's homes. A monk is not even permitted to select what he eats much less take pleasure in his food. It is the monk's responsibility to take whatever he is offered by way of food, whether he likes it or not. Buddha taught that monks must not fall in temptation's way. So, in the case of Andy and the host, we can see that side to Thai hospitality, which Andy might interpret, as over-solicitous judged by his British upbringing.