There is no study I've read that "proves" the primal / paleo diet bad or dangerous for long term health. For short term (10 years?) health, go look at the "before and after" thread that is probably up to 1000 pages by now, or the success stories forum.
But if your mom believes that anything you can find on the internet is true, you'll have an uphill battle to fight. I say do it yourself for a while, get healthy, THEN tell people about it if you want to.