"Senator, I Have Worked with Professors at the University of Pennsylvania," I Say
"I know professors at the University of Pennsylvania. Professors at the University of Pennsylvania are friends of mine. Senator, you're no University of Pennsylvania Professor."
For the underlying story, see here:
"When I left the United States Senate, I became a professor at the University of Pennsylvania," Biden said. "And I've spent a lot of time—and the University of Delaware has the Biden School as well, so I've spent a lot of time on campus with college students."
Apparently Biden was given the title of Benjamin Franklin Presidential Practice Professor at Penn (in 2017, after the end of his Vice-Presidency), which involved him giving four speeches a year, for $390,000/year, according to PhillyMag (David Murrell).
For the underlying source of the quote, you young whippersnappers who don't know the great lines of my youth, see here.
UPDATE: Some commenters argue that Biden was technically correct to say he was a professor, given his title. But I think that misses the point: Quayle may have been technically correct when he had said "I have as much experience in the Congress as Jack Kennedy did when he sought the presidency"; Bentsen's response was that Quayle was still no Jack Kennedy, regardless of technical analogies of experience. Likewise, Biden had the title Professor (though I think it's rather misleading to describe yourself as a professor when your job doesn't involve substantial teaching or substantial research), but he's still no professor.