Personally, I try to set the stage - that we split the bill in the middle.

When I'm with a girlfriend who I know is long term (not just one or two dates) we usually do the whole, I pay for one meal, she pays for another - and it evens out but when it's our first date I'm not going to set the stage and the expectation for me to pay for every meal.

Just because you have a vagina does not mean you're somehow exempt from having to pay.