First of all, please note that there is not any single theory of social movements. Instead, there are a number of theories that seek to explain these movements. However, there are factors that are cited by a number of these theories. I will look at one of these—the perception of injustice by the subgroup that is at the core of the social movement.
One thing that many theories of social movements say is that the potential members of a social movement need to have a sense of grievance. They need to feel that they are being treated badly by their society. They need to feel that there are injustices that must be redressed. It is in this context that we should think about the reaction of AIDS sufferers (and gay rights activists more broadly) to the stigmatization of the disease.
When AIDS became stigmatized by the bulk of American society, it helped cause AIDS sufferers and gay people in general to feel that they, too, were being stigmatized. They could feel that their fellow Americans looked down on them because of their sexual orientation. They could feel especially aggrieved because of a lack of sympathy for them as they struggled with a deadly illness. Because of these feelings of grievance and injustice, they were more likely (say a number of theories of social movements) to fight back against those who stigmatized them and treated them unjustly.