I've been teaching recorder/music to a group of homeschool kids. They use a very fancy recorder that doesn't need forked fingering to play Fa, so it's very intuitive to play using solfege. I love it. As I've been trying to explain to the children why we do this crazy thing, I've come up with some funny stories. My favorite is to tell them that we're learning the relationships of the notes.
Imagine you have a group of girls and boys. Helen, Simon, Lily, Derek, and Shaylee. We can guess at the male or female status of them based on the names. But can you guess why Helen and Simon should not date? Because they are related.
Imagine you have a group of kids and adult women. We tend to memorize the children's names and simply memorize the women by their relationship to the women.
The relationship between Do, Re, Mi, Fa, Sol, La, Ti, and Do are predictable. Mom, Dad, Brother, Sister, Aunt Uncle tell you the relationship of each member to the others in a family. To describe altered relationships in families we use terms like "half", or "step". In music we use "sharp" and "flat" to describe these accidentals.