I’ll make this short and sweet.
‘They’ is a plural pronoun. It is not to be used to refer to a single person. It is only to be used to refer to a group of people.
An example is necessary to illustrate this point.
Unacceptable: “Somebody is going to get their arm broken.”
Acceptable: “Somebody is going to get his (or her) arm broken.”
There are myriad other examples. Just listen to people speak. They misuse ‘they’ and its derivative forms far too often.
I was grading third year comm law essays, and made comments about ‘they’ being a plural pronoun, my students said they knew that was the case, but one argued that ‘they’ was coming into common usage as a singular. And she was right, it is. But that doesn’t mean I have to agree and accept it.
In a similar vein, ‘you’ is also a plural. However, in this case, its singular equivalent is ‘thou,’ which is difficult to use properly with its derivatives, ‘thee’ and ‘thy.’ I think I have them figured out, but ‘you’ is so ingrained as a singular it is too much of an uphill climb.