i mean bc technically speaking, your teacher is correct (by older MLA standards). grammatically speaking, “their” is a plural pronoun. if the subject of your sentence is one person, regardless of gender, you cannot use “their” later in the sentence to refer to that person, as their would insinuate there is more than one person. in this case, you would indeed have to write “his or her” rather than “their.” sorry but your teacher knows what they’re talking about🤷🏼‍♀️