The Fox News host Sean Hannity has been very upset.

Mr. Hannity is often very upset, at things like the past friendships of President Barack Obama; the suspected political leanings of his former colleague Megyn Kelly; the resignation of Michael T. Flynn, President Trump’s former national security adviser; and the tweets of media reporters from rival news organizations.

But the primary target of his anger in recent days has been Ted Koppel, a veteran news anchor and contributor to “CBS Sunday Morning,” which last weekend broadcast a clip from an interview with Mr. Hannity that the Fox star did not like at all.

The interview was conducted by Mr. Koppel roughly three weeks ago, Mr. Hannity said on his show Monday night, and had been presented to him as an opportunity to discuss the political polarization in American life. But only a minute or so of the full interview was used. And it looks as though it may have been the part that Mr. Hannity found the most insulting.

The night before the segment aired, CBS News posted online a part of the interview in which Mr. Hannity described his upbringing, which he said shaped his views. But in the televised footage, he was shown complaining about socialism, liberalism and “angry snowflakes,” right-wing slang for liberals that conservatives see as easily upset.