'I'm not going to explain myself to those nitwits'
This might be a reason why Hanna was referred to as arrogant. In 1961 she attended the trial in Jerusalem for war crimes committed by Adolf Eichmann for The New Yorker magazine.
The film focuses on this part of her life. She has a 'wow' moment during the trial. Eichmann's defence was he had taken an oath of allegiance to the Nazi leader Adolf Hitler and was only following orders. Aurendt concluded that he was an ordinary man doing his job and coined the phrase 'the banality of evil'. He wasn't evil, just a man following orders without any thought.