Final answer:
In 1968, the reaction of white Americans to the Civil Rights movement, which involved a backlash and resistance to further racial equality advancements, convinced many Black people that the majority of Whites opposed their aspirations for first-class citizenship.
Step-by-step explanation:
The element that convinced many Black people in 1968 that the majority of Whites opposed their aspirations for first-class citizenship was the broader response of white Americans to the Civil Rights movement's advances. In the wake of the Civil Rights Act of 1968, many whites felt that the problems of racial inequality had been sufficiently addressed. However, Black leaders like Malcolm X pointed out that de facto segregation and economic inequality persisted. The response of white Americans and their growing fear that their status was threatened by the advancement of minorities indicated a backlash against the aims of the Civil Rights movement. This revealed a disconnection between the laws aimed at ensuring equality and the norms and beliefs held by many white American.