I mentioned in another thread what it's like to live with a narcissist, how they absolutely cannot stand losing to anything or anyone. They will say anything to try to twist the narrative so that they're the winner/hero. They'll make up crap on the spot if they feel threatened with losing--or if they actually do lose. They don't care if it's true or not. They don't care if it's relevant or not. Or if it's cruel or not. It's an injury to their egos when you show them to be wrong about something. So they don't sulk about or resort to self-pity--they lash out, and they don't care about anything except winning in that moment, by any means necessary.
They'll say it, if they think it will put them back on top.
I mentioned how my own narcissist mum does this. I can't even count the number of times I've torn apart idiotic assertions she's made, and she invariably comes back with some vicious thing to tear me down rather than admitting she was wrong. And I'm not kidding about vicious. Things like, oh, "You think you're so smart? Well, you're fat and ugly, so you're obviously too stupid to know what you're talking about."
She really says crap like this when she's losing an argument, because she hates losing that much. She cannot bear it if anyone sees her as not being smarter and better than everyone else--at everything. Even her own children are fair game to tear down if they don't treat her like an Omnipotent, Omniscient goddess uber alles.
And yes, that's a big reason why I refuse to live closer to her than 300 miles. I'm actively suicidal if I don't.