>why not stick to his and her

the simple answer is that so many people obviously want a change. they feel that "his" and "her" are gender specific and so exclusive. why be exclusive if you can be inclusive?

>use the speaker's gender as the referent

i don't follow why using "his" if you're male and "her" if you're female is natural, if you're not writing about yourself.
this seems to confuse things more. what if you don't want to indicate your gender? what if you're somewhere in between genders? what if there's more than one writer?

i think the sound of "their" needs time for our ears to get used to it. but they surely will. stravinsky was once considered agonising.