My 4-year-old son, Emmett, swallows a spoonful of cereal and asks me if I know what a gentleman is. Surprised, I tell him I have some idea; then I ask what the word means to him.“A gentleman lets girls go first,” he says, explaining that every day at naptime all the girls go to the bathroom before the boys.His explanation, along with the quiet solemnity with which he delivers it, is completely endearing and yet it makes my heart ache. This adorable little boy, who is only beginning to learn the ways of the world, just got his first lesson in sexism — and from a teacher who, I don’t doubt, believes she’s doing something wonderful for womankind.She isn’t the only one.

I've taken the word gentleman to mean "respectful", not "chivalrous".

Is that an incorrect usage of the term?

the author makes that point at the end.  I think you are right.