http://m.huffpost.com/us/entry/562f8bc7e4b00aa54a4b26dd
If I reecall, back when Kappa Sigma resigned one of their main gripes was that as an NIC member, they were being forced to pay for initiatives and programming that essentially duplicated things they as an individual fraternity already had in place.
I think there's also a feeling that NIC should be acting as more of a fraternities as independent entities advocate, rather than just rolling over and playing dead for the schools when there are issues.
ETA: In this case, it seems support of the Safe Campus Act is a sticking point. I understand what this act is trying to accomplish, but a better idea than legislation would be educating students and the administration on why the whole "rape culture"/men vs. women mindset is so effed up, and that responsibility and respect for everyone (including yourself) should be the order of the day.