People under 18 are the responsibility of their parents ... sure that's only under American law and that the law of humanity suggests that we all have a right to protect ourselves, but there is a point at which society chooses to say "you can't make wise decisions" regardless of whether the kids actually can.
Why not lower the driving age to 10? The drinking age to 15? Society decided that at 16 a person can start taking on the responsibilities of driving. Society decided that at 19 you can possess a handgun. etc.
There is some reasoning behind it, obviously, but it cannot be compared to prohibiting firearms from people on university campuses who otherwise carry legally off university campuses.