My girlfriend has been suffering from her family's toxicity for years and talks to me about it regularly. I finally snapped and insulted her family. Her sister overheard everything, repeated it to them, and since then, my girlfriend refuses to stay with me.
I am frustrated because I didn't say those words out of nowhere: it was a reaction to the suffering they inflict on her, which she constantly shares with me. She is now extremely angry with me, even though I only told the truth about them. She is stuck in a loyalty conflict toward people who are destroying her, and her sister is using my words to push me out for good.
How can I make her realize that my anger came from a place of love and protection for her, rather than a desire to hurt her family?