I think the intent here is to make a differentiation between "boys" and "gentlemen" - and "girls" and "ladies". To me, using the latter in each appropriate case is telling them I expect a high level of manners and sportsmanship. I don't see anything sexist about it.
I've known lots of boys and men who weren't gentlemen, and lots of girls and women who weren't ladies. In fact, I married one once - and yes, it was a woman, not a man (not that there's anything wrong with that).
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Yom HaShoah
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