I think the "first" thing is silly, too. That said . . .
Gamma Phi Beta was the first of the NPC sororities to use the word "sorority" in referring to itself, although not from the very beginning. To quote from our history:
After the installation of Beta Chapter at the University of Michigan in 1882, Syracuse faculty member Dr. Frank Smalley coined the word "sorority" especially for Gamma Phi Beta. It has been used ever since.
It was Professor Frank Smalley who coined the term 'sorority' for Gamma Phi Beta. "Translate 'fraternity' into its real English equivalent of brotherhood and think how that sounds when applied to a society of women. Why then should the exact Latin equivalent be regularly so used?"
"The word 'sorority' or 'sisterhood,' moreover, is precise and definite and means exactly what we wish to denote when speaking of a society composed wholly of women."