Most folks who want gun control haven't thought about it (maybe haven't had to think about it) beyond just the general idea that fewer guns probably means fewer school shootings.
I think most of them do want freedom, but they don't connect the idea of freedom with the right to bear arms. 

 Correct. Freedom means different things to different people. One can mean actual freedom, while another is for people to live the way they demand. Words can be the same, values diametrically opposed. For example "freedom from poverty" or "right to affordable health care"