How to answer questions like "Aren't you happy?"

[Alan]

I would suggest that you accept it as a linguistic difference, though, no doubt, ultimately a culturally-related one.

English requires concord of positivity/negativity between the interjection (yes/no) and the verb phrase. Thus a simple combination of positive and negative ("*Yes, he isn't!", "*No, he is!", etc.) is not normally possible, whereas, in many oriental languages, the interjection functions independently of the verb phrase to denote simple agreement or disagreement with the collocutor's proposition.

Some European languages, however, do distinguish between two different kinds of 'yes': in French, 'yes' when agreeing is oui!, while when disagreeing it is si! , and in German the words are respectively ja! and doch!, (although in both cases these may still accompany only positive verb phrases.)

Good luck getting that across!