Why does Apollo agree to grant Phaethon proof of his origin?

Apollo agrees to grant Phaethon proof of his origin to reassure him of his divine lineage and to quell Phaethon's insecurities about being the son of a god. This promise is motivated by Apollo's desire to support his son and demonstrate his love, despite the potential consequences of revealing their relationship. Additionally, Apollo hopes that by granting this proof, Phaethon will find confidence and a sense of belonging in his identity. Ultimately, this act sets the stage for Phaethon's tragic journey.