I am supportive, however I know girls who have been *****, harassed and accosted, and don't want my girl to experience that kind of horror. Not over protective, but realistic. It's a mad, mad, mad world.
I may provide a sidearm to make me feel better about it. I did teach her some basic knife fighting skills, and she is not afraid of defending herself as she participates in "Israeli" fighting instruction at a dojo of some kind. Should something happen to her, I will go to prison, and I don't want that, either.