He's arguing the Peloponessian War was the greatest war up to that time, and that means it has to be greater than a) the Persian Wars of the early 5th century, and b) the Trojan War, which is taking on Homer and the entire literary tradition. I'm using the Crawley translation. Thuc. 1.1.3.

For though the events of remote antiquity, and even those that more immediately precede the war, could not from lapse of time be clearly ascertained, yet the evidences which an inquiry carried as far back as was practicable lead me to trust, all points to the conclusion that there was nothing on a greater scale, either in war or in other matters.

He has to address the earlier great wars to make his point that his war is the greatest. Hence his estimate of ships and manpower at Troy (1.10.4):

He [Homer] has represented it [the Greek force] as consisting of twelve hundred vessels; the Boeotian complement of each ship being a hindered and twenty men, that of the ships of Philoctetes fifty. By this , I conceive, he meant to convey the maximum and the minimum complement....

His point is that the Peloponnesian war involved SO MANY MORE people than the Trojan war, and this was entirely because of the money Sparta and Athens had to spend compared to the old Mycenaean states (1.11.1). Cicero 500 years later said money is the sinews of war. Thucydides is making the same point here.

The other thing is Thucydides is really writing a political history. Addressing the mythological past allows him to discuss the political development of Greek prehistory in a way that helps him explain the war he is writing about. He offers a complete explanation (probably wrong, but it's the best he could do) of the development of the polis as a political entity, which is central to a political history of the Peloponnesian war.