Mr Neil challenged the right-wing pundit’s views on abortion, the tenor of political debates and the Middle East before Mr Shapiro cut the interview short in frustration.
“Frankly, I find this whole thing a waste of time,” he said.
“You can think whatever you want of me, frankly, I don’t care.
“I don’t frankly give a damn what you think of me since I’ve never heard of you.”
Before he ended the exchange, the pundit also accused Mr Neil of being “of the left”, which appeared to leave the presenter, a former editor of The Sunday Times, baffled.
On Thursday Mr Shapiro, a former Breitbart editor, acknowledged that he had been unprepared for the interview and unfamiliar with the presenter’s work.
“As I’m not familiar with him or his work, I misinterpreted his antagonism as political Leftism (he termed the pro-life position in America “barbaric”) – and that was apparently inaccurate,” the pundit wrote on Twitter. “For that I apologise.”
After the interview aired on Friday he attempted to poke fun at the exchange.
“[Andrew Neil] DESTROYS Ben Shapiro! So that’s what that feels like,” he tweeted.
The joke references the titles of a series of YouTube videos which purport to show Mr Shapiro “destroying” fellow commentators in debates.
“Broke my own rule, and wasn’t properly prepared,” he added, posting a link to an article supposedly addressing the issues Mr Neil had raised.
“Still, it’s Neil 1, Shapiro 0.”
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