The gender pay gap is poor excuse for men paying for dates. I think the ratio is around 83%? So why not agree to pay 83% of what he has to pay?
Why should men pay for dates? Simple, because it's the first date and social norms compel him to pay. No other justifiable reason.
A question of respect? Respect goes both ways. Men are not the only players. Ever heard of a foodie call? I know, I know. #notallwomen. Neither gender is above reproach.
Over time a couple should share the expenses of dating. A woman in a long term relationship who is unwilling to share the expenses of dating is not likely to be willing to share the expenses of living. My advice is to avoid such a woman.