This post is adapted from some comments I made on a feminist blog in response to complaints about men asking this question.
I think the problem is that a lot of men, despite their privilege, feel intimidated and dis-empowered by the dating scene. It is a legitimate human behavior to seek companionship and love. When guys want to know how to express their interest in me without being threatening, invasive, or objectifying, I'm glad they're asking. I want companionship and love too, and I want it from people who care about not being creepy.
Here's the relevant thing most men don't know about being a woman: for nearly all of us, personal safety is a constant concern, and unknown men automatically register as a potential threat. To illustrate this, let me describe two exercises from rape crisis team training. In one exercise, we divided the white board in half. On the first half, the men brainstormed all the things they did to protect their physical safety. After several minutes, they had listed maybe three or four things; they would wear seat-belts, try to be aware of their surroundings, maybe avoid some neighborhoods at night. On the second half, the women brainstormed the things they did for their safety; this half of the board was covered. We carry our keys like a weapon when we're out walking; we study martial arts; we check the backseat of our car for strangers every single time we drive. We double check our locks and carry whistles or weapons. Some of us don't go out alone at night, and there are some places we never go alone at all. We are careful about what we wear, and where our drink is, and who we associate with. Do all women do all these things all the time? Of course not. But trying to avoid getting raped is, on average, a far more substantial part of the female experience than most men realize.
In the other exercise, the instructor picked a male volunteer and a female volunteer. She set them at opposite sides of the room, and asked them to walk towards each other. When they got close, the female volunteer blushed and ducked out of the way. We tried it again. . . and again. . . and again; the results were virtually always the same. Now, this was a truly kind and decent guy; he was donating thirty hours of his life to learn how to spend more of his time comforting the families of rape survivors while they waited for their loved ones in the hospital. Plus, he was cute, and nice, and had a great sense of humor. On top of this, it's hard to imagine a safer situation. However, he was a male and bigger than us--and that was enough to make him physically intimidating.
Obviously there are circumstances where picking up on someone is never appropriate. However, I think "you don't ever ask women out or tell them that they're pretty" is a totally counterproductive thing to say. It's better to explain that:
(1) Non-creepiness is all about letting her have the power in the situation--the power to leave, the power not to have to deal with physical threats, the power to avoid social or professional reprisals, the power of being listened to and respected like an actual human being--in short, the power to say no without inconvenience or harm of any kind
(2) Certain situations--approaching her while she's alone, at night, after drinking, in an elevator, in an isolated area, in a professional situation, etc.--carry implicit threats that men often aren't consciously aware of. . . and becoming aware of these implicit coercions can help them to be better men, and more attractive to boot
(3) If there isn't a situation where you are sure she feels/is safe and powerful about being asked, don't ask her out. This is the feminist way.