To illustrate how the stigmatization of social movements arises from its micro-foundation---the emotional confrontation, I model the process of such stigmatization on social media using an evolutionary game with two sub-populations---the participants of a social movement and outsiders in the general public. Based on the critical assumption of ``hostility as retaliation'', the members of the movement, who are hostile toward the general public, and haters in the general public reproduce each other. Suppose there are enough such hostile members so that it exceeds the stigmatization threshold. Then, the social movement is stigmatized and locked in conflicts with haters outside the movement. The stigmatization of a social movement can be a self-fulfilling prophecy. When there are initially enough haters, even if a social movement is peaceful at the beginning, the speed at which the movement becomes hostile under outgroup pressure will outpace the rate at which it can win public support, and finally induces the stigmatization equilibrium.