I always felt like saying if "he or she" took too much time and was unnecessary.
"They" will replace Him and Her! It might even be you! (If I ever refer to you in 3rd person)
My guess is that the initial response by MisterTea was an attempt at language policing, and this whole thread is a waste of time.
I think he/she will become outdated soon, if it's not already. I don't think anyone really anticipated there'd be a global debate about gender identity. Regardless of how anyone feels about that particular topic, it's not going to go away. Either everyone naturally shifts to the more inclusive "they" or people will continue to clamor for it.
Matt Levine's not alone in his use of "she/her" - it's actually fairly popular in modern technical writing, I've found.
It's never been 'he', except in sexism such as 'when the doctor comes he will examine you' (with the doctor's identity and hence gender unknown, but assumed male by profession).
Seriously, read anything more than about fifty years old. The 1918 Strunk & White¹ stated, "Use the masculine pronoun unless the antecedent is or must be feminine." They argued against inclusive pronouns in the 70s when E. B. White (yeah, the mouse guy) was in charge of the style book, and didn't start recommending inclusive language until the 2000 edition.
The Chicago Manual of Style originally didn't mention it because it was so ingrained in the English language. It only started discouraging its use in 1982, and didn't condemn it until 2010.
Edit: I guess I should state right here that I'm not advocating for default male pronouns in writing. I think "they" is the best replacement. But I was taught "he" and adapted to "he/she" over the years. "They" really only seems to have become prevalent over the last decade or so.
¹That's Strunk and White the style book, not Strunk/White slash fiction.
This might make a good subject for a RobWords video, actually.
But yeah, I get what you're saying. I don't have any explanation for you, other than he/she was what I was taught in the 80s in Oklahoma public schools.