These cowardly people who start shooting always go to gun free zones like schools, churches, and malls. They are scared to go where some one else might have a gun.
While they are certainly despicable people, I don't know that "cowardly" is a fitting adjective, as most of them don't intend to come out of it alive. Going into something in which you do not intend to live is not truly cowardly, although taking a bunch of other people with you is surely not an attribute. I mention that because people often refer to suicide bombers as being cowardly, and I can't help thinking that walking into a building with a bomb strapped to your chest is a lot of things, but cowardly isn't one of them. I think they choose gun-free zones because that improves the chances that they'll be able to take a bunch of other people with them before someone with a gun finally arrives. At that time, they often kill themselves, but I don't know if that's cowardly either. In a sense, perhaps it is.