But that's not what they said. They said he lied about being a professor at UPenn. That's simply incorrect

Biden is not a professor. He was given the title of professor. Biden was not schooled earning the degrees to become an actual bonafide professor.

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To become a professor, you must first earn a bachelor’s degree and then attend graduate school to receive a master’s degree in your chosen field. Holding a master's degree qualifies you to work at a community college. While in school, you should maintain a strong academic record, develop close relationships with your professors, and take part in internships. Exploring assistant teaching opportunities in your field, such as graduate assistant positions, is a great way to obtain experience in the classroom. Those who want gain tenure track as a professor at a university need to earn a doctorate in their field.
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ziprecruiter.com - What Is How to Become.

I did not find any evidence Biden earned a Masters Degree.

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Sen. Joseph R. Biden Jr., his Democratic presidential campaign battered by charges of plagiarism in his campaign speeches and in a law school paper, admitted yesterday that some of his boasts about his college academic achievements were untrue, including the claim that he had finished in the top half of his class in law school.

In a videotaped exchange at a campaign coffee gathering in Claremont, N.H., last April 3, Biden also claimed that he had attended law school at Syracuse University on a full academic scholarship, that he had been named the outstanding student in the political science department as an undergraduate at the University of Delaware, and that he had graduated from Delaware with three undergraduate degrees.
In a statement yesterday responding to a story in the current issue of Newsweek magazine, Biden admitted that these claims were "inaccurate."
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washingtonpost.com - Biden academic claims inaccurate