Saturated fats are more STABLE than unsaturated fats. The chemical structure of saturated fats is not easily damaged by things that will easily damage unsaturated fats, such as light and air. Hence why your high-quality olive oils are sold in a dark green glass or other opaque container? It’s to keep light from damaging the oil. Ever wonder why coconut oil doesn’t smell rancid from sitting out on the counter without a lid on it but a vegetable oil like corn or soybean oil will? Air oxidizes those oils and makes them rancid. What separates the saturated fats from the unsaturated fats is the presence of a hydrogen bond at every instance of a carbon in the chemical structure of the fat. When there is a double bond in the chain of carbons, it creates a more unstable structure, which you can see when a fat is liquid at room temperature: the group of unstable fats together form a liquid versus the group of stable fats together which form a solid or semi-solid.

Seed oils are extremely high in monounsaturated fatty acids (MUFAs) and polyunsaturated fatty acids (PUFAs) all different ratios of MUFA’s to PUFA’s, all of which are prone to oxidation, PUFAs most significantly. You wouldn’t want to cook with fish oil or other oils dense in PUFA’s, for this reason. MUFAs are pretty easy to damage as well (olive oil is very high in MUFAs).
So, which fats ARE safe and recommended for cooking?
It’s safe to assume, however, that most naturally occurring saturated fats are safe to cook with, while most unsaturated fats (called oils because they are liquid at ambient room temperature) are unsafe to cook with and are most ideal for cold uses if appropriate for consumption at all. Remember that man made trans-fats are never healthy to eat: Crisco, Earth Balance, Smart Balance, Benecol, Margarine, Country Crock, I Can’t Believe It’s Not Butter and others claiming to be a coconut product but it actually contains soybean oil!
Check out this chart of common (but not all) cooking fats & oils ranking them in order of best to worst for cooking.