As with most things involving the human body and nutrition, it's a bit complex.
Here's a good primer on fat from Mark's Daily Apple. It turns out that, with almost every health concern, it's the "..grains, legumes and sugars..." that pose a much bigger threat.
Yeah, that's right: grain (i.e., bread, pasta, etc.) are really not what you want to put into your body.
Grass-fed meat? Butter? Coconut oil? Turns out these foods are much more comparable to our ancestral diet.
Even if we just focus on saturated fat (which many people assume is worse that unsaturated fat), recent evidence suggests that there isn't a link between saturated fat intake, and heart disease.
There are a plethora of resources you can check out for more information about ancestral diets, protein/fat intake, and how those link to improved health. Here are a few: