My girlfriend wants an open relationship

Problem/goal: i just saw her typing here on reddit asking people how to ask me to have an open relationship.

Context: The reality is that I can't even entertain the idea. Thoughts of it make me cry, and l experience anxiety that leaves me breathless. I care deeply for her and want her to have the freedom to live her life as she wishes. However, the thought of her being with someone else causes me immense pain.

Previous attempts: nada. Walked out once i confronted her.