It's obvious Dia doesn't want to be seen as a dainty girl so she said she's not a girl although biologically she's obviously a girl or technically female as far as we can see. The author can do the okie-doke on us and she/he/it is a crossdresser, but I'm putting my money on it's a personality thing given the chaos she wrought in the tavern and her fiery disposition. She was probably raised around a bunch of guys so thinks she's one of the guys or something along that type of strong-headed, don't treat me like a girl/damsel trope.