I (F26) want to call it quits with a new bf (M34) after I found out he badmouthed me to his sister

TL;DR: Boyfriend badmouthed me to his sister last year and I just found out she hates me. I am thinking of calling it quits as it was over a misunderstanding he overreacted to anyway.

Ok this isn’t the ONLY event or incidence why I’ve had enough, but it definitely broke the camel’s back so to speak.

My boyfriend (M34) Jerry and I (F26) met a few years ago at a beach resort abroad. We lived in the same country but opposite sides. We stayed in contact and the majority of the communication was flirtatious and he expressed desire to date. We agreed not to because of distance. I got a job in the same city last year (not for him, just an offer) and we started going on dates October-November. December we made it official.

There were few hiccups and misunderstandings throughout our distant communication. The one that led to the situation with his sister was following:

My best friend Marcus was visiting me from my home city. He stayed with me for two weeks last summer. One day Marcus got a bit too drunk at a mini golf course and when we got home he passed out on the couch, where he slept during his stay, and snored extremely loud. I was a little sunburnt and tipsy so I went to lay down in my bedroom and tried to nap. I kept snoozing but waking up to the snoring and gave up. I scrolled my phone and got a text from Jerry asking how was golf. I told him it was great but I can’t nap because of Marcus snoring.

He went “…”. I’m like what? He asked “how do you think I feel when you tell me there’s a guy in your bed and meanwhile I’m here all in love with you”. Of course I was a little pissed he assumed such, but corrected him about Marcus being on the couch. He didn’t respond for a few days then just said “ok”.

Fast-forward to Easter when he took me to meet his sister and her family (their parents have passed away) in another city. He was really excited about it as his sister is the closest person to him. I could tell she didn’t like me but I figure she just doesn’t know me yet and it’s her little brother so she’s being protective. We visited for a few hours and when he was driving back home, I asked him if he noticed his sister doesn’t seem to like me.

He said yeah she for sure doesn’t, she thinks I’m a floozy who hangs with guys and lets them casually crash at her place while in the talking stage with others. That I don’t care about anyone else and that I’m just “using and playing Jerry”. I was fucking stunned. I’m like how did she get this impression and he told me he had been really upset about the snoring guy on my bed he had turned muted my messages and talked about it with his sister while he was visiting them. So that was the few days he didn’t respond. He said he had tried to correct the misunderstanding with her but she stuck to her view of me.

So not only did he jump the gun but he badmouthed me to his sister, who CLEARLY hates me. She didn’t like my hobbies, my job, my ethnicity, nothing, and it only makes sense if she thought I was a shitty person.

I said I want to break up but he thinks I’m overreacting since everything else (for the most part) has been okay. He’s begging me to stay, but this bothers me to no end.

FYI Marcus and I are only friends and there has never been anything between us romantically or sexually. I dated Marcus’ older brother in high school, who died in a car accident while we were together. Marcus got severely depressed and dropped out of school. I supported him through this time and he returned to school and managed to graduate. This created a deep bond between us.