My girlfriend told me she's polyamorous... I'm not. How do we make it work?

SoEsoteric
We're a new couple, only a few months into our relationship and she tells me she's polyamorous. She also told me I was the only partner right now.

I told her that wouldn't work for me, and that if she told me there was another guy I wouldn't be afraid to end our relationship but I want us to work. She started crying, She exclaimed "nobody understands me/accepts me."

Are there ways we can make this relationship work in the long run, or are we better off separating? I don't believe in Polyamory, mainly do to my own insecurities (jealousy and such) but also due to the fact that her previous ex apparently cheated on her. How can someone who has left a partner for cheating alright with having multiple partners?

Ultimately I'm lost because i've never been in this situation and want to make a relationship work.
My girlfriend told me she's polyamorous... I'm not. How do we make it work?
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