My girlfriend called me a racial slur during an argument. Is that a good enough reason to break up?

Anonymous
We were arguing over her older brother. What happened was her friend called her to let her know that he was found on a dating website. I have to explain this so you could understand why I laughed. Her friend had called her during a lunch date and it wasn’t just an ordinary site. Her friend told her “please don’t judge me but I found your brother on sugar daddy dating site.” My girlfriend was pissed off because he has a girlfriend of 7 years who my girlfriend is close to. I couldn’t hold in my laugh. I don’t know why I bursted out laughing. It’s mainly because her friend said “don’t judge me..” and also how her older brother was on a sugar daddy dating site because he works at an auto parts store making $10/hr so why is he wanting to be a sugar daddy? I felt so bad for laughing but I couldn’t contain it. It caused a huge fight where she ended up calling me a “beaner.”

I am wrong a bit for laughing but I’m only human.
My girlfriend called me a racial slur during an argument. Is that a good enough reason to break up?
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