I really should have guessed the answer to this, but it's basically the same phenomenon as Western academic regalia. According Wikipedia, hakama were a common designated uniform for female college (ish) students from the Meiji to early Shouwa period, and they've managed to linger on until now as graduationwear.

Incidentally, although this is also from Wikipedia, the world-famous sailor suit high school outfits date back to the late 1800s for male students (the collar a few years earlier) and the early 1920s for their female counterpart -- which is to say, as militarism really began to get a-chugging, the nation clad even its female young in navy uniforms.