Take a look at this sentence:
Everyone needs to hand in their assignment to the teacher.
Is there anything wrong with it? Most people would say no, and I would agree with them; however, if you’re obsessed with having perfect grammar, you might not like it. Here’s the problem: their is supposed to be plural, and everyone is singular. (If you don’t believe me, please note that needs is in its singular form.)
In order to solve this problem, some people prefer the following:
Everyone needs to hand in his assignment to the teacher.
But what if you are referring to men and women? What if you don’t know the gender and don’t want to sound sexist? In these cases, the grammar lovers out there might say his or her assignment, but that could come off as too formal. Furthermore, most English speakers use their naturally and don’t even see a problem here.
Regardless of which way you think sounds best, however, this situation raises some interesting questions:

  1. If you believe their is only plural, why does English not have a singular possessive determiner?
  1. If you believe their is plural and singular, why is there only one word for both?

The short answer to both these questions is this: it is not easy to add function words to a language. If something is missing, it is unlikely a new word will replace it.
Let’s look at some more sentences to drive home this point.
I saw a dog at school.
I hear dogs barking.
The dog I saw yesterday was huge.
The dogs in my neighbour’s yard are barking.
Looking at these sentences, we can see two things:

  1. There is no indefinite plural determiner.
  2. The definite determiner is used with both singular and plural nouns.

Again, we see that English is lacking determiners, and if you’re like me,this might make you wonder what else it could be lacking in? Well, it has weak case marking and weak subject-verb agreement, and I am sure smarter people than me could name a lot more. Yet, despite these missing parts, English functions perfectly fine.
So, is English missing something? Maybe. But I would say you can’t be missing something you obviously didn’t need in the first place!