This view comes in three basic varieties. The individual determines morality. If the individual determines morality, then if I believe it is morally permissible to steal your stereo and beat up your girlfriend, it is permissible for me to do it. But it is not permissible for me to beat up your girlfriend. Therefore, the individual does not determine morality.
Society determines morality.
Not at all. When an American university student protests against South Africa's policy of apartheid, he is assuming that morality is not determined by society. It is transcendent of cultures. All of our greatest heroes have been men and women who have stood up to society's wrongs and appealed to a morality that is transcendent to society in order to demand change. If society determines morality, it is always morally wrong to criticize society.