You are pursuing again. Doesn't work. You gave her an opportunity when you asked her out. She refused.
Fairly good answer when you told her to go ahead and date.
This woman has demonstrated again and again she goes the exact opposite of what you say or want. Seems to me that would mean that you have to tell and show her you don't want her and that you are done. You aren't giving up the OW on facebook. End of story.
Her pattern then is to chase.... You seem to have a hard time really letting her chase. I don't understand why, since it seems to be the thing that works so well.
Go back to "I have been doing some thinking and I want this over with. I don't love you in the way that I should. I think it is best that you and I both date others. I am not giving up other woman on facebook so there really is nothing more to talk about. It just won't work. I realized that I am not interested in even trying anymore.
You have a woman that takes the opposite position that you want or take.
Is it really worth the price? I don't think this is really about the OW. IF you got rid of OW she would then say you didn't do it soon enough or who knows what. She takes the opposite stance. When people are like that then the best thing to do is to take the opposite stance of what you want because then they take the exact stance you were trying so hard for them to move to.
I don't see what you lose by getting tough and kicking her to the curb. She is trying hard to make you feel dumped. The dumper is always in charge. Be the dumper.