>>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?<<

First, 'play'fully--what do you mean, play devil's advocate??

Serious, now--Tsuwm, you have just caused me to go thru a
thinking process that led to an embarrassing realization.
I have always been taught to object to using their as a
singular. But I have always accepted his as a neutral, because that was already in place (in use) when I was in
school. Seemed just fine to me, that's the way things were.

But your post made me realize (again) that the world did not begin with my birth! I imagine that when his first crept into use as a singular, there were probably rantings against this, just as in my school days there were rantings against using their as a singular, and...just as I now rant against using 'guys' to address females!

...and the language goes on...