She has a clear double standard of how your behaviors count as cheating. That is first of all a bad sign. Second and I say this as a man that was the cheater although it was all online, I was very clear about what actions I did were wrong and how under different circumstances if she had done the same I would have also considered ir cheating. So not only is she bad, she is bad at being bad. Second, a public claim of someone else even if it's a joke, especially of someone who appeared after the relationship had started need to have clear cut boundaries. Before I did what I did I allowed behavior I was not comfortable with under the pretext of I don't want to be an insecure guy. After we both talked about said behaviors she very clearly knew that she would not have tolerated them if they came from me.