I always assumed there was some tradition to cutting your hair short before going to war, because long hair would present numerous liabilities - more maintenance, potential visibility issues, potential to foil cover/disguise, and potential vulnerability in hand to hand combat. And there is a lot of military tradition to a short haircut, though I’m not sure how much is based on the above reasoning. But I’m not a historian so maybe this is just a bad interpretation of Mulan or a random teacher passing on low quality education.