The main event that led to the rioting by Buddhists against the Diem regime was the self-immolation of a Buddhist monk named Quang Duc on a street in Saigon. This happened on June 11, 1963.
This monk burned himself to death in protest of the policies of the Diem regime. Ngo Dinh Diem and his family were Catholic. The vast majority of people in Vietnam were Buddhist. Even so, Diem discriminated against Buddhists. An example of this came when he did not allow Buddhists to conduct public celebrations of a major religious holiday in the city of Hue. This led to protests that were repressed harshly.
In response to actions such as this, Quang Duc killed himself. His example, in addition to the insensitive (to say the least) reaction of the Diem regime (Diem's wife welcomed suicides like that, using the word "barbeque") led to huge unrest among Buddhists in Vietnam.
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