Why can't I let her go despite all that she did to me?

I'm having a hard time letting go of my ex. We had been together for a year and a half before breaking up in May of this year. We started seeing each other again towards the end of July before ending it again at the end of September. I feel like she used me as a back up plan in case someone else didn't come along because she was texting another guy while we were seeing each other again. She claims she only wanted to make it work with me and just thought this other guy was cute, but wasn't interested in him. I caught her on a few lies and found a text to her mom that didn't match her previous claim. She found out I had seen this text to her mom and she told me she felt weird and awkward now. Eventually, she told me she wanted space, but wanted me to remain as her best friend so that we might try again if she sees a change in me and that I can be mature. I guess a change being me not caring if she texts other guys while we're seeing each other, I don't know. Well, now she is seeing this other guy that she was texting and is going around telling people that I was being immature and stressing her out and a bunch of other crap. Her texting another guy is what actually led to our first breakup too. I know that this should make me write her off completely and never give her another chance, but somehow I can't stop thinking about her and the possibility of it working out. I want to get over her and settle on never talking to her ever again, but there's part of me that wants to hold out for her. I know that if she came to me tomorrow wanting to fix things again, I would take her back. Just last week, she texted me saying that I'll always be her best friend and she even came over to see me one morning to tell me to have a good break. She kept giving me long hugs and even blew me a kiss goodbye that morning. I want to let her go for good, but I don't know why it's so hard to go through with it even after all she did and say.
Why can't I let her go despite all that she did to me?
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