Everyone submittedWait. the grammatically correct sentence above implies the students were only male. It could be considered sexist. Also, it could be flat out wrong if some of the students were, in fact, female.
theirhis assignment late.
Everyone submitted his or her assignment late.The sentence above is grammatically correct and is no longer sexist. But it's also awkward. To correct the catch-22, remove the indefinite pronoun and substitute the word all. Then use the plural pronoun as you originally intended.
All of the students submitted their assignments late.More opportunities to remove sexism from writing
Policeman becomes police officer.
Fireman becomes fire fighter.
Army man becomes soldier.
Scuba man becomes scuba diver.
Mailman becomes mail carrier.
Repairman becomes mechanic.
Secretary becomes assistant.
One is a terrible replacement for sexist words
To write a grammatically correct sentence with the word one, you must use the word one consistently throughout the entire sentence, paragraph or work. It's a slippery slope. This can be difficult to maintain as a writer, and tough to tolerate as a reader.
One can improve one's writing if one would spend more time at one's library.A rule of thumb
To avoid issues with sexism and pronoun agreement, always write in third person plural.