I called my girlfriend a slut for dating her ex while being with me and trying to hide it, can I be forgiven, and what should I do?

Me and girlfriend were having a fight. We used to text and talk all the time, but she only texted very little after the fight. Weeks later, I find out she was spending time with her ex, and I got her to admit that she tried dating him when we were fighting.

She left me for another guy before, and she denied it was cheating, just disloyal. She also refused to cut off communication with her ex when i asked.

A day after she admitted to trying to date her ex, I snapped at her and said I should just break up with her forever, and I called her a slut. She isn't a slut, and hates promiscuous behavior.

Her ex told her that she has dropped down too low to let someone call her a slut. She breaks up with me and we get back together. She's somewhat distant with me now, and still spends time with her ex. She won't forgive me for calling her a slut, and acts like she didn't act disloyal to me twice.

I always try to make things work, but I don't know. I feel really bad for hurting her, and I regret it. But she won't cut her ex off, and won't forgive me or start treating me with love again. Should I keep letting her treat me like trash because I called her a slut? Is calling her a slut worse than her being disloyal to me? How do i fix this?
Updates
+1 y
We break up a lot, but we always get back together within the week. Is it still considered cheating if she "broke up" with me and tried dating her ex during that time? Thank u for all the responses, I think she gaslights me a lot and I'm trying to be a better person, so I always try to play it in my mind like I need to improve
Updates
+1 y
Yeah, I'm going to break up with her, I've been meaning to for so long, but she keeps apologizing and saying she will be better. I just needed others' opinion on this so I know that she's gaslighting me instead of me being a bad person.

She did not have sex with her ex, but I definitely feel like she tried to leave me for good, it's just that I'm the only guy who ever treats her well because she has trouble making friends and she also hates men
I called my girlfriend a slut for dating her ex while being with me and trying to hide it, can I be forgiven, and what should I do?
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