Your issue is quite common if one of you are either socially incompetent (many people are, both guys and girls), not in the mood (aka state), or simply if you don't have chemistry with each other. I know that I personally find it extremely hard to talk to people in general if I'm not in state - I simply have nothing to say, and I'm not interested in whatever
they have to say either. Some would say (RSD Tyler for instance) that it's due to insecurity, but I know that insecurity has nothing to do with it. Lack of interest has.
I also know that I easily get in state with people I have chemistry with. So if I don't click with someone, there will be no action. I have accepted this, and by doing so I feel much more relaxed and comfortable in social situations. I don't "have to" say anything. Silence is good too. And as RSD Tyler has said (I think), self acceptance is 50% of... Something. Inner game maybe?
On the other hand, pickup is about putting some effort into social interactions, trying to make a good impression and keep a conversation alive. This is the other 50%. Almost all people have something they love to talk about, and when you get a girl started she will most likely never stop and you wish she could just shut the f up. Consider it your mission to find out what the girl loves to talk about. If it is something that bores you, you can feel good about NOT having sex with her, and thus "fail" in pickup terms.
CHAT
