The prince chooses to leave his tiny home planet because he has grown unhappy and restless.
In Chapters 8 and 9, the prince tells the pilot about his love and dedication to a beautiful rose that suddenly sprouted on his planet one day. The prince watered, tended, and cared for the rose, granting her every request in order to make her happy. However, the prince says that the rose never reciprocated his affections, and he found himself exasperated and ready to explore the universe beyond his tiny home.
Ironically, the prince’s decision to leave is what prompts the rose to confess her love for the prince, yet he still leaves anyway.
It is implied that the prince finally realized he was far too immature and inexperienced to truly love the rose, and that he needed to venture away from home in order to grow up.