There are a couple of major problems here with arguing that armed civilians don't stop mass shootings. One is that when armed civilians are present, they often stop mass shootings before they can become mass shootings. One of the criteria Mother Jones used to define mass shootings is that "the shooter took the lives of at least four people." So then, consider the following
Mayan Palace Theater, San Antonio, Texas, this week: Jesus Manuel Garcia shoots at a movie theater, a police car and bystanders from the nearby China Garden restaurant; as he enters the movie theater, guns blazing, an armed off-duty cop shoots Garcia four times, stopping the attack. Total dead: Zero.
– Winnemucca, Nev., 2008: Ernesto Villagomez opens fire in a crowded restaurant; concealed carry permit-holder shoots him dead. Total dead: Two. (I’m excluding the shooters’ deaths in these examples.)
– Appalachian School of Law, 2002: Crazed immigrant shoots the dean and a professor, then begins shooting students; as he goes for more ammunition, two armed students point their guns at him, allowing a third to tackle him. Total dead: Three.
– Santee, Calif., 2001: Student begins shooting his classmates — as well as the “trained campus supervisor”; an off-duty cop who happened to be bringing his daughter to school that day points his gun at the shooter, holding him until more police arrive. Total dead: Two.
– Pearl High School, Mississippi, 1997: After shooting several people at his high school, student heads for the junior high school; assistant principal Joel Myrick retrieves a .45 pistol from his car and points it at the gunman’s head, ending the murder spree. Total dead: Two.
– Edinboro, Pa., 1998: A student shoots up a junior high school dance being held at a restaurant; restaurant owner pulls out his shotgun and stops the gunman. Total dead: One.
These are just a few examples of mass shootings being prevented. I'm sure there are many more that meet this criteria. But, as you can see, in every incident, the would-be shooters were stopped short of killing four people because an armed civilian—or in some cases, an off duty cop—was present.