Bathrooms are segregated by gender because victorians thought women deserved better than unsanitary holes in the ground, so they made actual bathrooms for them when women started to work in factories.

By the time enough men realized they wanted indoor plumbing at work too, the tradition had been established that women had separate facilities and so the separation stuck.

(And now it’s just the slow process of redoing every public bathroom on the planet to be gender neutral. Which is harder than it should be since transphobes love telling horror stories about trans women so they can police all women.)