There is something about this that skeeves me out as well, and it's not simply discomfort at the idea of doing it. It's the idea of manipulating others for drinks. It reminds me of begging, almost, the whole trying to get free stuff from others. Also, it sounds like leading men on far enough to get them to buy you a drink; it sounds like making them think you're interested, even if you don't actually promise anything. I'm not so fond of things that might inconvenience others, nor the idea of getting drinks from others because I've led them to believe something false.
I believe the male version is to get a girl's phone number? What skills does this require? I'd guess confidence, the art of conversation, body language, assertiveness, initiative, etc etc. Everything that's already been listed. However, what skills does convincing a man to buy a girl a drink require? What would make a man want to buy a girl a drink? I'm getting the impression of a great deal of flirtatiousness.
I feel that a more equivalent challenge would be for a girl to get a man to accompany her to one of her hobbies, like a knitting group or an orchestra concert or a rationalists' meetup. That way, she has to present her hobby well, get the guy interested, and he has to be interested in something other than sleeping with her. It will require more communication than sexuality, and I feel it will teach the desired social skills better.
Above I argue that this is an equivalent of at least one part of PUA, and explain the subtext behind why it seems skeevier.
Recent brainstorming sessions at SIAI (with participants including Anna, Carl, Jasen, Divia, Will, Amy Willey, and Andrew Critch) have started to produce lists of rationality skills that we could potentially try to teach (at Rationality Boot Camp, at Less Wrong meetups, or similar venues). We've also been trying to break those skills down to the 5-second level (step 2) and come up with ideas for exercises that might teach them (step 3) although we haven't actually composed those exercises yet (step 4, where the actual work takes place).
The bulk of this post will mainly go into the comments, which I'll try to keep to the following format: A top-level comment is a major or minor skill to teach; upvote this comment if you think this skill should get priority in teaching. Sub-level comments describe 5-second subskills that go into this skill, and then third-level comments are ideas for exercises which could potentially train that 5-second skill. If anyone actually went to the work of composing a specific exercise people could run through, that would go to the fourth-level of commenting, I guess. For some major practicable arts with a known standard learning format like "Improv" or "Acting", I'll put the exercise at the top and guesses at which skills it might teach below. (And any plain old replies can go at any level.)
I probably won't be able to get to all of what we brainstormed today, so here's a PNG of the Freemind map that I generated during our session.