The narrator of "Battle Royal" does indeed have difficulty delivering his speech, and it's not hard to see why. He's just been forced to undergo a humiliating experience in front of a crowd of drunken, baying white men who clearly have no respect whatsoever for the young man or anything he has to say.
Reading out the class speech at his high-school graduation is one thing, but reading the same words in front of a hostile crowd is something else entirely. At the high-school graduation, the narrator could be assured of a warm reception for his speech. But here, in front of all these drunken racists, he has to take great care over every word that he speaks, and that makes him incredibly nervous.
Somewhat inevitably, he stumbles over his speech, saying the words "social equality" instead of "social responsibility". Immediately, the crowd explodes in uproar. The very idea of an African American saying such words out loud in front of white people is almost unthinkable to them. "Social equality" sounds perilously close to "racial equality" which is the last thing that white people in this segregated, racist society would ever be prepared to accept. So the narrator collects himself and says that he meant to say "social responsibility".