As I see it there are quite a few instances when you would want to wear this shirt. First, when you have friends who are too shy to introduce themselves and you want to be their wingman. Second is when in a bar and you want to cleverly get rid of that good-looking guy in your group so you wouldn't have to compete with him anymore. :-D Lastly, when you want to get rid of somebody who's been tailing you by helping them meet other people first.
Here's that Have You Met Ted Game that Barney created to help Ted, well, meet a girl.