okay, I'm going to play devil's advocate (even though I'm an adiabolist) and ask the obvious question:

what makes distorting the meaning of 'they' by making it singular better than distorting the meaning of 'his' by making it neutral?

e.g., everyone should follow his own feelings vs. everyone should follow their own feelings (or, in the first case, as discussed elsewhere, the speaker/author can use her personal pronoun).