The author is suggesting the following through this use of verbal irony: He exposes how weird it was for the handicapper to be involved in the role of achieving equality
Verbal irony is a type of literary technique employed in storytelling whereby the speaker's words are not in harmony with his intent. We see a good example of this in the statement, “I think I’d make a good Handicapper General.”
In this statement by Hazel, one may think that he is praising the role of the General but the opposite is his intent because he exposes the folly of the General's role in promoting equality in a society that did not pay attention to people's rights.