grammatical number - In the sentence 'This means everyone should have their turn to say something.' , why is the noun not used in plural?

I am preparing for an exam, and came across the sentence below.

'This means everyone should have their turn to say something'

And I wondered why this sentence has no grammatical errors.
Isn't the noun 'turn' countable? hence should be used in the plural form or should have the indefinitive article 'a'?

For me 'everyone should have a turn to say something' sounds correct.

Thanks in advance!