You don't have any power OVER women. You don't have any control OVER women either.
Control of the external world is an illusion.
All you can really control is your own actions and your emotions. Women try to manipulate us because they can hijack most men's emotions to the point men cannot control their actions. Women do this by playing on our fears of loss and lack of confidence.
It really is all a front, though. Women are incredibly insecure or they wouldn't have to resort to such manipulation. Walking away works better than you actually think it does. And it will work on a woman IF SHE'S ATTRACTED TO YOU.
You may never see the effect though. Remember, women manipulate. They can't accept reality as it is, so they try to change reality by trying to change the emotional states of the men around them. If it doesn't work, usually they'll move on to try it with the next, weaker guy. Most women won't let on how much it stings, but again that depends on their attraction level.
You walk away because it's healthy, particularly to have and enforce boundaries. You walk away for you. Some women chasing after you when you do walk away is only a bonus but should not be the reason.