Rodriguez says he was reinvented by President Richard Nixon. How do you know this is an exaggeration and therefore irony?

because Nixon was not referring to him directly but to the entire Hispanic community.

Explanation:

Note what the original excerpt says,

"Because of colonial Mexico, I am mestizo. But I was reinvented by  President Richard Nixon. In the early 1970s, Nixon instructed the Office of  Management and Budget to identify the major racial and ethnic groups in the United States. OMB came up with five major ethnic or racial groups.  The groups are white, black, Asian/Pacific Islander, American Indian/Eskimo, and Hispanic."

We can see from his statement that the Office of Management was tasked by President Richard Nixon with identifying several groups..., not Rodriguez directly, but the Hispanic community was among those included. Because of the fact that his ethnic group was included, Rodriguez exaggerated the actual direction from Nixon.

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