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You cannot use logic in affairs of the heart.
She has convinced herself that you killed it by screwing another girl.
Her extreme reaction shows that she felt a sense of ownership over you that her words earlier did not support - this shows that she is a poor communicator.
She broke up with you and then admitted that she still wanted to be cross when you acted like you'd broken up - this shows that she doesn't know what she wants.
Even if you work everything out, you'll still have a relationship with a poor communicator that doesn't know what she wants.
This is recipe for disaster.
The coolest and most adult thing you can do (and the only one that I can see has any chance of granting you peace, sanity, and maybe the chance of a healthy relationship with someone in future) is to walk away and go cold turkey for a while.
If you cut off all communication with her - do not initiate emails, respond to any she sends you with "thanks for getting in touch, I'll let you know" and then answer whatever genuine questions she has, but don't get drawn into dialogue about who did what and who said what; if you do this, you will both have a chance to calm down.
Once calm (took me and my ex a couple of months, ended in amicable divorce, but previous cases for me and others ended in rehabilitation as friends or lovers) you can get on with your life, she can get on with hers.
Possible outcomes of this calm strategy:
1 - You both realise you still care for each other
2 - You both realise it's time to move on
3 - one of you wants to be together the other doesn't
1 & 2 are win/win.
3 results in resentment or at best a pity fuck.
If you want a relationship of resentment and hatred, keep chasing her, because right now you're at 3 - you cannot get from 3 to 1 by nagging.
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Overhead, the Albatross hangs motionless upon the air,
And deep beneath the rolling waves,
In labyrinths of Coral Caves,
The Echo of a distant time
Comes willowing across the sand;
And everthing is Green and Submarine
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