Let's take it from the other side's perspective: if I was a college administrator against on-campus carry (by students? by anyone?), what would be my biggest buggaboos?
1. Guns are evil/only have one purpose/etc. standard antigun diatribe.
2. There is a higher frequency of suicide attempts in college. Most are unsuccesfful, but you add a gun...
3. Drunkeness + gun = uh-oh
4. A lot of love/jealousy/break-ups in this age group, often without the maturity to handle it well.
5. Over-21 students (men) lording it over the under-21s who can't get permits, creating a lower class of underclassmen.
6. If I let carry go through, and there's even ONE incidence of abuse resulting in death or crippling injury, then alumni donations dry up and I'm SO looking for a job as head of the English Department at University of Nowhere. If I'm lucky.
Not sure how you counter these fears. #1 is the standard emotional "no guns ever!" attitude that we encounter so often. #6 works because, at the present time, neither alumni nor the media consider college administrators complicent when a murderer kills college kids that the administrators (or state law-makers) kept unarmed--so at the moment it's all downside, no upside to a change of policy.
Unless...we can promote the examples of U of Utah and other carry-okay campuses (in VA?), and show that those fears are baseless--the way that FL CCW eventually dominoed a lot of other states into shall-issue once the success was apparent.