Panhellenic means all Greek even though, technically sorority isn't a Greek word, it's Latin...anyway..lol
By promoting Greek spirit, you are promoting the existence of the Greek system at your school. Just think of what your sorority/fraternity stands for. The other groups may have different symbols and rituals than yours but we are all Greek.
Sororities and fraternities depend on each other to promote our concepts of sisterhood/brotherhood, philanthropy, scholarship, etc.
Even though individual sorority members may not get along, it is important to promote a united front. As Eric Conrad, TKE, has said on another post, someone is at the top of the list and someone is at the bottom. If the bottom sorority/fraternity goes away, that leaves someone new to be the bottom group. Eventually, that may lead to no Greek organizations on campus.
Good luck with your application. It can be a tough yet rewarding job.