A small note on British school terminology · 1:19am August 16th
You can't have a female headmaster, at least not in Britain you can't. I've seen it used that way a few times now, including in excellent stories, and it's always thrown me off for a second, so I'm wondering whether Americans use the term in a more gender-neutral way. But here, it's not like "chairman" which in the past was sometimes used even when the post was filled by a woman. In this country, a female head is a headmistress. The gender-neutral term is "headteacher" or just "head". ("Principal" is used to some extent here but isn't always a direct synonym for head, so beware.)
interesting
questioning my grammar, I find myself not fussed about it either way, though I would definitely prefer "chairwoman" over a neutral "chairman"
McGonagall is most certainly a Headmistress. Having some fun with her character in Sweetie Belle - Hogwarts Exchange Student.
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"Chair" is a neutral option. At least in the UK, it's reasonably common.