Not paying for the date is fine. Assuming that it makes you a better person to default to not paying for the date is disgusting. If you're going for equality, then you stick to logical considerations:
Which of you is wealthier?
Who asked and who accepted for the date?
Who picked the restaurant or film?
If you're the asker, picker of establishment, and/or wealthier party then you should probably begin with offering to pay. Deciding your choice of action uniformly based upon defining every party you could date as 'the female I am on a date with' is significantly more sexist than what is ultimately an act of generosity... functionally, if you want to decide as equal parties, the course of action is this:
Consider who should pay for it via a variety of factors, none of which is gender.
If yourself, begin by offering to pay; if your partner, ask how she would like to have it paid.
Work something out, then look back to ensure the decision is based upon a compromise between your desires rather than assumptions of philosophy or tradition.