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Maybe for validation of herself. She is unsure of what she wants to do
Exactly.
The reason why girls insist on "staying friends" after a break up is because they need self-affirmation after a break up. They want you to keep giving them attention, they want you to keep chasing them, they want you to have a hard time getting over them, they want to stay on your mind, they want to monopolize your consciousness. You must deny them this at all costs.
You are right, you need to go no-contact, but you CANNOT tell her not to contact you. This is OVERTLY communicating that you want to go no-contact, it will simply make you regress into betadom and possibly cultivate emotional resentment in her. If she KNOWS you are intentionally ignoring her, the spell is broken.
Next time she texts you, ignore it. When she calls you, ignore it. If you bump into her and she asks why you've been ignoring her calls tell her "Sorry, I was busy with a lot of stuff, haven't had time to text and call and stuff." If she texts you consistently, respond to half of them in a brief and witty way but never send concurrent messages.
As far as getting over her, I have a 3 step process.
1. Control your thoughts, don't let them linger on her. As hard as it may seem, FORCEFULLY make yourself think about other things. You have a world to conquer - women should not delay your dreams. The more you train your mind to stop lingering on negative thoughts, the easier your life will be.
2. Fuck other hotter women. Seriously, busting into a girl hotter than your girlfriend is like assaulting your Oneitis with a SWAT team.
3. Invest in another girl. The reason why we hang onto lost loves for so long is because we have emotionally invested so deeply in them. A zealous christian wouldn't renounce his faith even in the presence of 20 hindu gods and would instead rationalize it as "God is testing me." The time, emotions, money, and other mental/physical resources we invest in girls we "love" create an attachment difficult to get over. Invest in ANOTHER girl to counter-act this emotional investment. Best case scenario, you have a new girlfriend and you can fix the mistakes you made in your last relationship. Worst case scenario, at-least it's not the same girl.