Jim Dixon -- on listening to that song again, via the link you sent me, the words you missed in the first verse were "If invited, she will holler: 'Take me to an ice cream parlor."

Guest Lou -- as to how it became a catchphrase, I woke up this morning remembering that my dad, whenever I complained that something popular (TV show, music, book, etc.) wasn't any good, he'd rejoin:

"Well, that's why they make Chocolate and Vanilla!" So maybe that's the origin?

(My dad was born in 1927)