Not a great answer but looks like the question is going to get closed.
Some cultures and some families just feel like a girl should never pay. In the US I know two girls whom their mother told them a girl should never pay.
I would just approach her about going dutch before you leave for the meal or drinks to avoid an awkward situation at the table. I think it could be as simple as "Would you mind going dutch?" Don't even say "dutch tonight" - put dutch on the table.
I would not give your reasons or try to present a case. She is going to go along or not.