Fats and Peroxidation
One of the biggest problems with lipids (fats, oils, cholesterol, and so on), especially the unsaturated lipids, is that the fatty acids in them become oxidized very quickly on contact with oxygen, creating free radicals, as described earlier. Free radicals are molecules that lack an electron, so they will take one from whatever source they come near. Ingested free radicals will, as they circulate in your body, steal electrons from healthy cell walls, damaging them in a process called lipid peroxidation.
Severely peroxidized lipids reveal the smell and taste of rancidity, but at much lower levels than are detectable by our senses, the free radicals present can be destructive to tissues, accelerating the aging process.
Since many of the foods we eat are prepared long before they are purchased and consumed, the amount of free radicals potentially available in your food is significant considering the time that has elapsed since the oils were pressed, the butter churned, and so on. But it is also likely that you will increase the amount of free radicals when you cook your foods. Even if you use oils that are low in free radicals, when you put them in the frying pan, where they are exposed to both heat and oxygen, you bring on massive oxidation and free-radical production.
It's not the lipids themselves that are dangerous, but the way they have been processed. For a long time eggs were linked with a high blood cholesterol count - an erroneous connection between dietary cholesterol and the body's independent natural production of cholesterol. Soft-boiling an egg in its shell is very different from frying or scrambling it with oils in a hot skillet; during boiling, the proteins are cooked gently without ever reaching the high temperatures of a skillet's surface, where they would be exposed to hot oils and oxygen.