Mistake Type:
Hyperbole
Exaggerating a point or a phenomenon well beyond what the facts or common sense would support, in order to evoke an emotional response.

Examples:
(from right) “The Democrats are trying to destroy the country.”
(from left) “Conservatives are making me fear for my life every day.”
About Hyperbole:
Hyperbole is very similar to exaggeration, but indicates an extreme form of exaggerating that may either be intentionally absurd or seemingly serious. Typically there is not an expectation that audiences will immediately believe the literal meaning; nevertheless, the effects are expected to work towards the advantage of the issuer.
One effect may be a strong emotional response that makes the statement memorable and pulls the discussion agenda towards the issuer. In other words, even if the statement isn’t immediately believed, it becomes a topic that people are more likely to talk about.
Another effect may be that audience members question their own prior beliefs. This is less likely if the statement is intentionally absurd and is easily recognized as a mere rhetorical flourish. But the more serious the statement seems, the more doubts and questions it may trigger.
Hyperbole sometimes can also be regarded as an implicit “dare,” as in, I dare you to contradict me. For example, if the argument is made that anti-trans laws are genocide, raising an objection about that might be met with accusations of indifference to transgender people’s human rights.
To the extent the statement is regarded as plausible, it leads the audience towards false beliefs. The issuer gets away with it because it’s too arduous to analyze or research the statement. Audiences looking to disrupt the hyperbole could simply ask some version of “can you tell me more?” or “not sure I understand your point, can you clarify X?”