This is The Immortal Bard by Asimov:
The physics professor, Dr. Phineas Welch, has gotten himself slightly drunk and begins speaking with Scott Robertson, a young English teacher. Welch announces, "I can bring back the spirits of the illustrious dead." [...] "So," he continues, "I tried Shakespeare." [...]
Eventually, Welch says, he enrolled Shakespeare in a night school class on Shakespeare's plays—taught, as it happens, by Robertson. At this point, Robertson begins to become genuinely worried. He recalls a bald man with an unusual accent, and starts to doubt whether Welch's story was all alcoholic fantasy. Timidly, he asks Welch what happened, and the physicist explodes with anger. Shakespeare had been humiliated, he says, and Welch had to send him back to 1600: "You poor simpleton, you flunked him!"
(Previously answered here)