A consequence of the Muggle and Wizarding worlds growing closer together is that Squibs and the Muggle siblings of Muggleborn wixen are no longer cut off from their worlds of their families.
There is no longer a hard and fast line between the two worlds.
There is, however, a line between their respective educations. Hogwarts isn’t equipped for non-magical students, and Muggle schools simply can’t teach Wizarding culture.
The solution, one of many changes to the newly liberated Wizarding world, is a new school in a middle ground, to give those children (and even adults) footing in both worlds. It (mostly) follows the Muggle requirements and curriculum, giving appropriate credits for the students to use in the Muggle world, but also teaches Potions, Herbology, Care of Magical Creatures, and History of Magic, to give a Hogwarts-like context for students to use in the Wizarding world. The school also makes much more room than Hogwarts does for wixen whose magical powers develop later or slower than others.
It’s first Headmaster? Aberforth Dumbledore.
Thanks @luthorslesbian for this super fun conversation, out of which grew this amalgamation of things with both of adding as we went. <3 You’re a star!