Is it okay to breakup with a person because of their inability to admit to mistake?

I am a straightforward person , I don't shy away from admitting my mistake. There may be some instances where I deny it but at the end of the discussion , if I think it was my mistake , I admit to it.

I have even said sorry for things that wasn't my fault. But I can't anymore. I have noticed that my girlfriend NEVER admit to anything. Even for small stuff , she never accepts when she is wrong.

Is this reason strong enough to breakup. I am not even exaggerating , she has never said the words "sorry" to me
Yes breakup
No , it's just your girlfriend's personality
Talk to her and give her chance to improve
She can't change , breakup
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Is it okay to breakup with a person because of their inability to admit to mistake?
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