I think the core of Lightbrite’s answer is a Gemara.
The Mishna in Nedarim 35b says that Person A that has been forbidden (through a Neder) to provide benefit to Person B, may still teach Tanach to Person B’s sons and daughters. In the Gemara that follows there is a dispute about how people are allowed to take money for teaching Torah at all: Rav says that a person can take pay for watching the children so that they don’t run around and get into trouble outside (see “Rashi” Nedarim 37a); Rav Yochanan says for teaching them the trop (i.e. how to lein which is not Torah d’oraisa).
Later (Nedarim 37b) the Gemara asks why Rav Yochanan doesn’t hold like Rav that the pay is watching the kids. The Gemara answers because the Mishna said that one is allowed to teach Tanach to the daughters of Person B (despite the fact that one normally can be paid) but girls don’t need watching (because they don’t run around outside).
So girls don’t need school on Sundays because they behave without school!