Edith Hamilton is probably the most famous modern-day writer of Greek myths, but how did she become interested in transcribing these myths?
We can trace out some possible answers to this by examining the history of her life.
Her father encouraged her interest in the classics from an early age.
"My father was well-to-do, but he wasn't interested in making money; he was interested in making people use their minds"; thus, her father guided her towards the Classics, and, when she was seven years old, he began teaching her Latin, then French, German, and Greek.
She was dissatisfied by the teaching of classics in her university lectures.
According to [her sister] Alice, Edith was extremely disappointed with the lectures she attended. The lectures were thorough, but lost sight of the beauty of literature by focusing on obscure grammatical points. "Instead of the grandeur and beauty of Aeschylus and Sophocles, it seemed that the important thing was their use of the second aorist," she said.
-- Adventures Abroad: North American Women at German-speaking Universities, sourced to her sister's autobiography Exploring the Dangerous Trades: the Autobiography of Alice Hamilton, M.D.
She encountered the tales of ancient Greece when she was young, and loved them throughout her life.
"I came to the Greeks early," Hamilton told an interviewer when she was 91, "and I found answers in them. Greece's great men let all their acts turn on the immortality of the soul. We don't really act as if we believed in the soul's immortality and that's why we are where we are today."
Upon retiring, she moved to New York City and wrote and published various articles about Greek drama. Although she was long recognized as the greatest woman classicist, she was 62 when she published her first book, The Greek Way, in 1930. For 50 years before that her "love affair with Greece had smoldered without literary outlet".
Putting all of this together, we can work out a rough outline of the story. Her father got her interested in the ancient Greeks and their works in the first place, and she never lost her abiding love for them. But she was sometimes frustrated at how poorly they were taught in the west, and this inspired her to create better retellings of them so that others could appreciate them as well as she even without being able to read ancient Greek. As we know, she was successful - her books being used to this day for teaching youngsters about ancient Greek mythology and culture.
She grew up loving ancient Greece and its culture.
I found an excerpt of an interview, I cannot copy paste (it's an image) but here it is.