Explanation: I believe since it includes a group instead of a singular person of an unidentified gender, their would be correct. Non-singular: Everyone should make their bed.
Singular example: A person might do this to impress his or her boss.
Everyone should make their bed. It is hard to explain but I think the correct explanation is that you said everyone, which includes all people, boy and girl. Because of this inclusive word, you can't use his or her
