"Someone has forgotten their book". Why can we use 'Their" and what's the difference if instead of "their" we use "his/her"?
they and its derivative forms in this case because we don't know the person's sex. Since English doesn't have a gender neutral singular pronoun, "they" has actually become one:
Singular they is the use of they, or its inflected or derivative forms, such as them, their or themselves, to refer to a single person or an antecedent that is grammatically singular. It typically occurs with an antecedent of indeterminate gender, as in sentences such as:
- "Everyone returned to their seats."
- "Somebody left their umbrella in the office. Would they please collect it."
- "If a person doesn't want to go on living, they are often very difficult to help."
He is used when referring to a male, and she to a woman, so we can't use them when we don't know the person's gender, such as when we say "someone."
It's actually a complex issue; a lot of people consider the Singular They as informal. I personally think that this is the best option that exists in English. You should avoid it in formal writing by trying to think of another way to say the sentence without "they" (rewriting), because of the people who may think it's ungrammatical (e.g. "Someone has forgotten this book" has the same meaning.) But if you must use a gender-neutral pronoun—don't fight with it and use "they."
Since the issue is complex and everyone has a different opinion, you can use
he in formal writing and be backed by linguists who share the same opinion, but it'd sound awkward when using it informally.
A nice article about the subject can be found in here, in case you'd like to see more information.
In situations where we don't know the gender of the subject they is often used as a way of saying "his or her" or "he or she" even though it's incorrect because there is only 1 subject. In these situations a singular subject must be picked, or something like "his or her" can be used. Historically he was commonly considered the default singular go-to, but the speaker can choose her instead if he likes (See what I did there?). For example:
Someone forgot his bag.
The use of their should be used for plural unknowns only. For example:
Everyone forgot their bags.