Let's start with your side of the interaction:
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I opened with a neg/teasing opener.
I responded "That's the problem with some girls today."
You opened with negativity and then followed up with even more negativity. You get back what you put out and this is the reason she blew you out.
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I don't understand how she knew I was a PUA
She must know about the pua subculture and recognized the neg-style opener.
IMO some of her accusatory statements were either true or close to the truth, such as 'women say one thing and do another': We've all heard a woman say "I just want a nice guy with a sense of humor." Meanwhile in general they (not all women of course) get wet for and desperately want to get with the suave playboy who doesn't take any shit.
This interaction is even further proof that when you drop all the gamey tactics and just talk to a woman like the human being she is, you can get the results that both you and the woman want (to get close to eachother and enjoy eachother's company) assuming she is interested.
Before you approach, don't think to yourself, "ok, time to go into pua mode, I'ma go hit on her now." Don't be trying to "get" something from them; instead think, "I'm the prize and I'm gonna go playfully chat her up and see if she's cool enough to chill with me."
But the thing is you can't fake that. That's why some guys have to rely on the crutch of routines etc. and don't see the results they want - because they actually don't feel themselves to be valuable enough; they don't truly believe and embody the "I am the prize" paradigm by feeling great about themselves and the future and by knowing without a sliver of doubt the immense value they bring to the lives of the select fortunate women they meet and decide to spend time with.
A while ago on this forum someone referred to getting "the hand" as a negative response from a woman. I literally had no idea what he meant by this (the girl putting her hand up as in 'talk to the hand') until thinking about it for a few minutes.
You can get wonderful and amazing reactions if you are open to just talking normally with them while subcommunicating sexual intent. There is no need for all the A1, B2, Attraction Stage tactics.
Also this was one girl. Don't let some girl affect your reality. And I am going to suggest something you will probably view as outlandish: Mentally THANK THAT GIRL. Her response was feedback for you: Feedback saying your opener wasn't on point and you may want to modify your approaches. As strange as it seems, she was helping you.
The moment you get out there, casually mention something to a girl about something going on in the immediate environment and she lights up, you will laugh at the notion of temporarily having let that girl at the bar affect your reality.