What should I do to convince her?

I have a beautiful relationship for 4 months. We love each other so much that we miss each other if we don’t see each other so much even in one day. I had had talked to my 16 year old student and she saw our messages. I am not a pedo, I didn’t do anything but to messaging with her. that was before her but she says that it is not right to talk to my student. I don’t say this is right and I was aware that I made a mistake. I tried to convince her for 2 days. She didn’t say anything but to break up. interestingly enough she let me hold her hand, caress her hair and kiss her. last day I said ‘I did my best and I love you so much’ saying that I accepted the break-up. kissed her many times hugged her and we cried. Should I give up on her or talk to her within severals days again?

What should I do to convince her?
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