Is this a good reason to break up?

I'm breaking up because I found out the real reason why his mother hates me. He's been complaining to her about me and elaborating things in our arguments. He's been telling her things I've never said such claiming I told him that I hate her food or that I think she's stupid.

I've been wondering for nearly 5 months why she hated me so much and my own boyfriend was the cause of all this. I'm going to break up? Would you break up to if your partner purposely lie about you to his/her parents, making you look bad?
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Note: not just that but I'm finding out he also said things about his mother she never said. So when he was with me, he was thrashing about his mother and when he was with his mother, he was talking bad about me to make her hate me more.
Is this a good reason to break up?
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