Which sentence is incorrect regarding the subject-verb agreement?

The sentence that is identified as incorrect in terms of subject-verb agreement is "Neither of the answers were correct." The key to understanding this error lies in recognizing that "neither" is a singular pronoun, which requires a singular verb to match. Therefore, the correct formulation should be "Neither of the answers was correct."

In the other examples, the subject-verb agreements are accurate. In the first sentence, "Somebody forgot their bag," it's acceptable in modern usage to use "their" as a singular, gender-neutral pronoun, which aligns with the singular subject "Somebody."

The second sentence, "Everyone should do his or her best," appropriately uses "his or her" to agree with the singular subject "Everyone."

Lastly, in the third example, "Both of the students lost his or her books," while phrasing could be modernized to simply "their books," it showcases agreement by pairing the plural subject "Both" with "his or her," acknowledging the individual ownership of the books.

Thus, the focal point for the incorrectness in the selected sentence centers around the mismatch between the singular subject "Neither" and the plural verb "were."