Yes, college campuses should be 'gun free' zones because there is no reason anyone should have a gun on campus. It would scare too many professors away. What if a professor teaches a controversial subject? If they know that someone in the class might have a gun, they will shy away from debates.
Most college campuses are already "gun free" zones, and how many instances of mass violence have occurred on campuses across the U.S.? How many of these could have been prevented or been less harmful if a student or faculty member was trained on how to properly carry and use a firearm? Yes, there is security around campuses, but they can't be expected to be everywhere at every time. You have to operate under the assumption the assailant knows where the police are when deciding where to attack. Could this attack, which did not involve a gun, have been prevented if a member of the student body had legally carried a gun in that area? I'd like to think partially as there is really no way to stop the car from driving in the crowd, but a responsible gun user could have stopped the man from harming people with the knife.
It is not always practical to implement complete gun bans in public spaces because there are some individuals who genuinely need to be armed at all times. However, these cases are very rare and it would therefore seem sensible to make reasonable restrictions on the carrying of guns on campuses.
Students have the same rights as their elders and non-student peers. The Bill of Rights allows individuals to have guns. States already regulate the minimum wage for a gun owner. Students and employees of colleges and universities may not want to be out of their dorms at night without some protection. Even campuses aren't safe places to be anymore.