Two things to consider as you read this:
1) This has no reference to how much money you make or spend. (An inexpensive date can be even more valuable than a very expensive one.)
2) I have approached men, but I do believe in the man being the distinguished leader of a relationship. (If someone is a leader, they had to take the first step or do something exceptional.) I state that from culture based on how I was raised, not as a statement for arguments. My culture isn't the only one in the world. Consider whatever works for you.
Do they already know each other? This matters. Let's say the girl and the guy have been good friends for a few years, and the guy wants to take it up a notch. He's decided that she's the woman he wants. When a first date is considered, they already know each other and they're already good friends, so in reality it's nothing different from what they've been doing for those few years as friends already. Therefore, why should he have to pay her way too? She knows what she's getting into just as well as he does. Years of friendship gives them a good foundation, and him paying her way isn't going to give her much to consider otherwise. (or vice versa with the genders; both ways apply) This is why I believe that it's ridiculous to say as a rule that one should pay for both if they both already know what they're going into. Each should pay his or her own way because both already know the investment. This is kind-of like going 50/50 once a couple has been in a relationship for a while.
It's a matter of the value of TIME, not money. If they don't already know each other, then the effects of investment into a possible relationship are unknown. The possibilities are endless - both good and bad. You can think of this like playing the stock market: you have a set amount that you keep as a minimum for yourself, and then you use the rest to make investments. With dating this comes into play on both sides: time and money. Time takes the lead, and here's why: the person being asked has to decide if the requested date is worth his or her time.
Example (I'll even use myself to avoid conflicts among users here.): If a guy I don't know approaches me in a public place and lets me know he's interested and wants to go on a date with me, the first thing considered is that I have a life apart from him. Is it worth my time to go out with this guy?
That said, since he's the one who is obviously interested, and since I know nothing about him, he needs to give me some reason to want to go with him over, say, spending time with my best friend - he has to show me that he's serious and wants to invest in a relationship with me. Regardless of what the date is - there are some dates that are even free, mind you - it's a matter of the time.
Wait, how's that? How is it about the time when you're saying he needs to pay because he's the one who showed interest?
Because again, I don't know him and I have a great life apart from him, so why not just go be with my best friend, or something else I like to do? Like, if the guy asked me to go to a music festival with him, for example, well if I have to pay my way, I'd rather just pick whom I want to go with and go with a friend. Chances are that whatever he asked me to, I wasn't planning on doing anyway. (The exception in this case is in the last two paragraphs.)
So my point there is this: if you're going to invest in something, it involves going a distance for whatever you're investing in, in addition to holding your own stability. If you're just holding your own stability, then you're not investing. Invest time, effort, and money wisely!
So what about the it's-not-about-money, free-date thing?
This is where, again, time takes the lead. That person still wants a reason to put you in their schedule instead of just taking up space on the calendar. Can this happen with a FREE date? YES! In this case, though, the investment is what you show up-front: no money, just YOU. Can YOU make YOURSELF seem pleasing enough for a date within this time when you first meet randomly?
For example, I met a guy randomly in the mall once - no previous knowledge of each other. He was very charismatic and good to talk to, but I had to leave because I had somewhere to be. Those few minutes that I had left at the mall actually turned into over two hours. That was the first investment: he gave me reason to even stay with him then instead of going to where I was headed next. So why not go on a free date with him? He discovered that I like art exhibits, and there is actually a free one in New Haven that he asked me to for a first date, and it was one of the greatest dates I remember.
Conclusion: If you're showing interest in someone, show that you're worth his/her time, keep in mind that time is more valuable than money, and make the investment to show the distance you're willing to go with that person at first.
Side Note: I am not offended when guys on this site get mad and call me a "gold-digger," especially since I am fortunate enough to have affluent parents, still probably have more than these guys do, and in a few years as a doctor I'm going to be making probably more than triple what these guys make anyway lol
So if you wanna argue it, I'll take it as that you admire my medical education and see my determination for striving through it. so thanks ahead of time :)