Learn Italian: Questo argomento non ti interessa? - Doesn't this topic interest you?

Argomento is a classic false friend! It means 'topic', 'subject', or 'theme'. If you want to talk about an 'argument' (as in a verbal fight), you would use a word like un litigio or una discussione.

Why do we use ti interessa instead of saying 'tu non interessi'?

The verb interessare works exactly like the verb piacere. The subject of the sentence is actually questo argomento (this topic), which is doing the action of 'interesting'. The ti is an indirect object pronoun meaning 'to you'. Literally, the sentence is asking, 'Does this topic not bring interest to you?'.

How would the meaning change if I moved the subject to the end: Non ti interessa questo argomento?

The core meaning is exactly the same, but the emphasis shifts slightly. Italian allows very flexible word order. By putting questo argomento at the very beginning of the sentence, the speaker is highlighting the topic itself, almost like saying 'As for this topic, doesn't it interest you?'.

If I want to agree and say 'No, it doesn't interest me', how do I answer this negative question?

You simply say No, non mi interessa. If it actually does interest you, you would contradict the negative assumption by saying Sì, mi interessa (Yes, it interests me). Italian does not have a special word for answering 'yes' to a negative question.