I don't know much about the other mythologies but with Greek mythology, myths were always used to "explain" something or "justify" something.
EXAMPLES:
The Rape of Persephone - The story of Persephone's rape, imprisonment, and reluctant release was used to explain why we have "seasons". Because Persephone partook of 6 pomegranate seeds in Hades' realm she was condemned to spend 6 months of every year at Hades' side as his bride. While she is in the Underworld, Demeter (Persephone's Mom) mourns her child and the Earth reflects her mourning (Fall/Winter). When Persephone is allowed to return to her mother, the Earth reflects Demeter's joy (Spring/Summer).
Narcissus and Echo - This myth is used to explain where the Narcissus flower comes from and why it is always found near clear water. Additionally, the unrequited love story between Echo and Narcissus is used to explain the "echo" phenomenon.
Arachnea - This story is used to explain where spiders come from. This story also contains a "moral" (like Aesop's Fables) that warns against pride and overinflated egos (sense of self-importance).
My suggestion to you is to keep it simple. If you have a passion for reading - create a myth about where the written word comes from, if you have a passion for being social (hanging with your friends, etc) - create a "moral" myth for how to keep secrets, deal with friend's controversy, etc. That kind of thing.
The teacher is probably just really looking to see if you "understand" what a myth is, not so much your skills/abilities as a writer of fiction. Although a sense of imagination and fluid writing would boost your overall grade on the project.
That's my two cents,
Celestial Beginnings (Leslie M. Crenshaw)