Honestly, some of it with the college age girls is immaturity and a competitive nature. Some of the actives who talked trash about other sororities behind closed doors in my chapter are now, at ages 45+, ones with the strongest Panhellenic spirit. Sometimes it takes age and a bit of wisdom to see how silly things we deem so important as an 18 year old are.
ETA: I will say my smaller school (15,000 students, so smaller than Ole Miss, etc) had a great Panhel spirit. We hung out with women of all different groups. I attribute some of that to living in a Greek Dorm, with all the sororities having a floor in the dorm, vs. having houses and being more isolated.