>>17843204 (OP)The three main sources for the Trojan War are Greek epics from about 800-500 BC, archaeology and Hittite tablets covering about 1400-1200 BC.
The Greek epics tell the story we're familiar with. The archaeology tells us there was a city in the area where Troy was supposed to be, which might be the city of Wilusa (= ilios? = troy?) mentioned in some Hittite documents. This city has multiple destruction layers, one probably from an earthquake, one from fire. And Hittite documents mention the 'ahi-yawa' with yawa probably derived from iลnes, archaically iawones (ionians, i.e. greeks). A Hittite text also mentions a king of Wilusa called Alaksandu (Alexander), a greek name. But it's impossible to determine if any of the destruction layers in Wilusa were due to a war with the 'yawa' and if so, whether this inspired anything specific in the much later Greek epics.
To answer your question: we don't know if there was a historical Trojan War, so we can't be as specific as getting into the nitty gritty of why it hypothetically started. Maybe there was a folk memory among the Greeks of wars involving Wilusa, but there's no way to check any of the specifics.