What makes a fat more vigorous in this regard? For one, how saturated it is. What is it saturated with? Hydrogen (H) atoms. A saturated fat is absolutely loaded to capacity with as many H atoms as it can take on. It's full and sedated and stable (much like the FRE after dinner). It takes a fair amount of energy to get a saturated fat up and moving around. On the other hand, a fat that's not saturated is more open to interaction. It's hungry. If you serve it some H atoms under the right conditions, it will chow down. (This is called hydrogen-ation.) If you serve it some oxygen (O) atoms under the right conditions, it will chow down. (This is called oxygen-ation, or in this case, oxidation.)
So, a saturated fat isn't going to be chowing down anytime soon. An unsaturated fat is, and will, in effect, become what it eats. If it eats H, it becomes saturated and stable. If it eats O, it becomes unstable and is primed to walk down the path of rancidity ruin.
This is one reason why manufacturers hydrogenate oils. Saturated fats resist rancidity. A cracker sitting in a box on a grocery store shelf that's made with partially hydrogenated soybean oil (the cracker, not the shelf) is going to smell fresher after 6 months than a cracker sitting in a box right next to it made with non-hydrogenated soybean oil (the cracker, not the box).
Saturation of a fat is only one guide in telling how vulnerable a fat will be to rancidity, with saturated (and fully hydrogenated) fats the least vulnerable, polyunsaturated fats the most vulnerable, and monounsaturated fats somewhere in between.
The following chart shows the degree of saturation of the oils found in the nuts that typically occupy a mixed nut bowl. Notice that most oils contain a mixture of different types of fatty acids. This is also true for butter and lard, which are referred to as saturated (fats receive designations based on their predominant fatty acids), but actually contain some unsaturated fat making them prone to rancidity.
By looking at this chart, can you tell which nut is more likely to go rancid before the others?
1 I use the terms oil and fat interchangeably. An oil just refers to a fat that is liquid at room temperature.