Why wasn't Cadet Seeger's hair cut short like everyone else's?

It's not sex discrimination. Women are allowed to wear their hair down as long as it doesn't pass their eyebrows or their collars. They can keep it longer if they're able to braid it or pin it up neatly allowing proper wear of head covers. They are not allowed to shave their heads unless they have dreadlocks when entering basic training. Dreadlocks are not permitted. It women can keep their hair tidy, professional, and not requiring regular "beauty salon" upkeep, they are allowed some latitude. Enlisted men don't have to keep their heads shaved either. For most it's a choice.

Oh, almost forgot. I think she was just emotional and made a mistake because he corrects her saying "Gunnery Sargeant, Ensign Seegar."