Possibly you should have looked it up before proceeding.
When you talk about using the 'plural they', you are of course obliquely referring to the fact that 'they' remains morphologically plural in all (correct) uses, however its usage to refer to a singular subject is well established.
It has been the preferred style for decades, an accepted style for centuries, and an existing style in English since so long ago that the language is barely recognisable.
If you can present an example sentence where using 'he' or 'she' is grammatically correct, but 'they' is not, then I would be interested to hear it.
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