Why does Herodotus allude to the ancient Greek tradition that the Spartan king, Leonidas, was a descendant of the demi-god Hercules

The ancient tradition regarding Leonidas' ancestry was part of the historical record of the Greeks, and in his Histories, Herodotus included all information that he gathered in his investigations of Greek history.

Herodotus (5th century BC) is known as "the father of history," because his writing pioneered the field of historical research. Indeed, we get the word "history" from him. He called his writing about the Greeks and their wars with Persia the ἱστορία (historia), which in Greek meant "investigations." We now call his book "The Histories," but it could be called "The Investigations." As the History Channel notes, in doing his investigations, Herodotus "listened to myths and legends, recorded oral histories and made notes of the places and things that he saw." In other words, Herodotus tried to include all the stories he heard, including popular tradition or legend.

Herodotus records the genealogy of Leonidas in a way that emphasizes he is a great man descended from an even greater ancestor. Here is the section from his Histories that gives that impressive genealogy:

Leonidas was the son of Anaxandridas, who was the son of Leo, who was the son of Eurycratidas, who was the son of Anaxander, who was the son of Eurycrates, who was the son of Polydorus, who was the son of Alcamenes, who was the son of Telecles, who was the son of Archelaus, who was the son of Agesilaus, who was the son of Doryssus, who was the son of Labotas, who was the son of Echestratus, who was the son of Agis, who was the son of Eurysthenes, who was the son of Aristodemus, who was the son of Aristomachus, who was the son of Cleodaeus, who was the son of Hyllus, who was the son of Hercules.