I enjoyed the chapter, but I don't understand why Dumbledor couldn't have simply said that Wizards and boys and Witches are girls.
After all:
In the Harry Potter verse it's impossible to be a male witch. Considering that you've taken liberties when it came to superheroes I think we should allow Rowling at least that much.
Also British society has a long and continuing tradition of having all boy and all girl schools. So having them mention both witches and wizards in the title of their school is perfectly accurate whereas "School for magic" not only goes against a tradition for alliteration in Wizard society but also be less clear in the name of the school.
Last but not least, remember that traditions were started for a reason and stopping a tradition for no good reason can be just as bad if not worse then continuing one.
It's only when a tradition is obviously bad or unproductive that we should toss them away.