Melanie and I just got involved in an in-depth discussion of music theory. The debate was why sharps and flats are both needed and why we can't just do all key signatures with sharps. After drawing out the circle of fifths and several keys and trying to transpose the key of A flat major into the key of G sharp major by just changing the notation of the flatted keys, we determined that it was because you'd have to use both C and C sharp in the same key. Which turns out to be the same reason I gave her in the start that she didn't like- the presence of double sharps, just under a different name.
That was surprisingly fun. I didn't realize that the music geek in me was so hungry to get out and play. Bless you, circle of fifths.