Final answer:
Phaethon searches for his father to learn about his identity and to validate his divine heritage, a common motif in stories for self-discovery.
Step-by-step explanation:
Phaethon suddenly goes in search of his father because he is eager to know his own identity and to confirm the truth about his divine heritage. His quest is driven by the need for personal validation and the longing to prove himself in the eyes of others who may doubt his lineage. This theme of seeking one's parentage and establishing one's place in the world is a common motif in mythology and literature, often representing a rite of passage or a journey of self-discovery for the character involved.