It’s never “her or his”.
Try saying that. Try writing it
“His or hers” is so ingrained that it seems natural “his” should always come first.
Maybe sprinkle in a few “her or his“‘s into your next term paper to make your professor reread the page several times with the sense that there is an error somewhere…
I actually consciously use “hers or his” all the time, or just the gender neutral “theirs/them” etc.
Also, it’s way easier to write s/he instead of “he or she” or “she or he.”