The simple answer to this has nothing to do with confidence or "having balls". It's a matter of NATURE.
Look to nature for your answer. I used to be an avid deer hunter (not so much anymore, but I used to be), so I spent a lot of time in the woods and I've observed a lot of different wildlife...mainly deer, so I'll use them.
Do you ever wonder why deer season is, well, a "season" in the various states? And why they choose particlar dates for it?
Well, part of the reason has to do with a thing called the "rut", which is the season where most of the little bambis are made.
They have the season during the rut because that is when the deer are stirring and the sexual drive is the highest during that time. So, while I'm deer hunting, I'm actually observing the sexual patterns of deer (sounds kind of sick doesn't it?).
The point I am making is that in watching these deer, one thing is almost always constant. Anytime you see a "doe" (female deer) you keep your eyes peeled because if you are seeing a bunch of does, you are almost SURE to see a buck (male deer) during that time. Why? Because the bucks are CHASING the does. And the does are always running from the bucks...but not running AWAY fromt he bucks, just running from them.
Why do they run from them? Well, because the buck that can "catch" her, is the one most likely not to be sick or most likely to have the strongest genes for her offspring. Without the chase, she wouldn't have a method for weeding out which are the weaker deer and which aren't, and in order to ensure the strongest possible survival for her offspring, she makes him chase her. Not only that, but this is also a time where you are likely to see the bucks locking antlers with each other. The more dominant deer is the one who's going to catch the doe.
Why did I say that? BECAUSE PEOPLE ARE NO DIFFERENT. We are just more civilized about it (if you can call it that).
We are each hardwired with a natural instinct for surival. We are each hardwired in such a way as to promote the best chance of survival for us and our offspring.
Men are hardwired to spread their "seed" across as many women as possible (much like the buck is trying to do during the rut) and women are hardwired to proactively preselect who will be the most likely to survive and be the most apt to protect and take care of her offspring.
So, a women CHASING a guy is unnatural because it voids this "natural" litmus test that is hardwired in her. Or rather, it'snot natural for a woman to do this, because of the way she is hardwired.
Hence, men approach, and females SELECT.
In short, it's all about natural selection and things that are hardwired into us as a species.