By insisting on paying her own way (at least) on the first date, a woman sends several important messages to her date. She is asserting her independence - and she can gauge her date's reaction to her independence (if his reaction is extreme, it signals that she could loose her independence in any relationship with him). Yet it also sends another, more positive, message: she is on the date to enjoy her date's company, not to gain access to his resources. If he accepts her as his equal, they have a solid base on which a future relationship could be built.

We're long past the says when men held all the financial power and women had to plied with sweet candies and lobsters. Men and women are equals in Western relationships. Thus, two people on a date can demonstrate their equality by sharing in the financial burdens of a meal. Besides, by sharing the financial responsibility, there are no untoward expectations or obligations. If there is no interest between the two, there are less hard feelings if one does not feel "owed" something.

If a woman contributes in a date by her presence, and a man contributes with his presence and money, the only way we could assert that this exchange of value is equal, is by attributing a lower value to the male.
Assuming this is not the case the proper thing to do is to go dutch.

If your date reaches for her wallet without having discussed it one way or another, I don't see any reason to prevent her from paying for herself. She may desire to do so for a variety of reasons, including a feeling of independence; in some cases, she may even be offended if you demand to pay the whole bill.

It is the age of equality according to CNN

Women are financially insolvent breeding mules. To expect that mewling milk spouts could afford the sort of meal required to flatter them is sheer fantasy. Even if they could, men should still pay. Men must demonstrate their power in society, of which money is a pretty ace marker. Because once that girl realizes you're interested in her enough to drop forty bucks on a lobster, their heart will be yours.

Anyone who plans and asks someone on a date should expect to pay for both parties. Expecting your date to pay anything is simply rude.

Most women date in order to find a mate. It is essential that while selecting a mate and a future father for her children, a woman must asses both the genetic potential and the behavioural patterns of any potential mate. (That is what most women do, even if they do not always reason it out consciously.) By expecting the man to pay for her meal, even though she may be more able to afford the cost than he, a woman will be able to observe his true attitude towards her: did he think that paying for her meal entitled him to take liberties with her, or did he treat her with the respect she is looking for in a potential life partner? If he sees her as a piece of 'meat' to be purchased in exchange for food, there is no point in pursuing a long-term relationship with him. Finding this our on the first date, before she falls in love with him, is prudent common sense. A man who behaves politely and with respect, even when faced with an unfair situation, is worth a second date.

A woman is doing the man a favor by being seen in public with him