Here is a 40-second advertisement from the UK Government regarding saturated fat:
Interesting to note (and Tom Naughton did as well in Big Fat Fiasco) that apparently saturated fat is a liquid in the refrigerator and solid at room temperature. And if you follow the logic that anything that clogs your drain-pipe will clog your arteries, probably leaves you with just H2O to consume.
The incidence of heart disease is not decreasing, yet we’re eating less saturated fat.
Also, invoking the logic that saturated fat raises cholesterol; and high cholesterol clogs your arteries; and clogged arteries cause heart disease; therefore a diet high in saturated fat causes heart disease is a logical fallacy (and one could argue that each link in this chain is unsubstantiated as well).
Drinking excess water leads to frequent urination. Frequent urination is linked to diabetes. Therefore, drinking too much water will give you diabetes.
There is an increase in sales of ice cream in the summer. There is a higher incidence of drowning in the summer. Ice cream leads to drowning.
There is an increase in the number of observed umbrellas outside when it’s raining. Umbrellas cause rain? No. They’re at the scene of the crime, but not necessarily the culprit.
A clinical trial in the 1970s tested the effects of a cholesterol-lowering drug called clofibrate, which lowered cholesterol in subjects. The trial had to be stopped because the men taking the pill had a 47% higher death rate than the placebo group. 
By the same logic invoked above, I can say that a low-fat diet reduces cholesterol, and lower cholesterol (via clofibrate) led to more deaths, therefore low-fat diets kill you.
Virtually every trial that tried to support the fat/heart disease connection has failed. What do good scientists do when faced with overwhelming contradictory evidence? They admit their hypothesis failed and they explore other questions.
If you replace saturated fat in your diet with cereal, skim milk, a banana and an orange, your LDL may go down, but your triglycerides will go up. Your HDL will go down. And now you’re at a higher risk of heart disease. These are better predictors than LDL, but they, too, have their limitations.
Also, More saturated fat does not mean less HDL, as many people seem to believe. In a meta-analysis of 27 studies on serum lipids (Mensink and Katan, 1992), the study noted: “All fatty acids elevated HDL cholesterol when substituted for carbohydrates, but the effect diminished with increasing unsaturation of the fatty acids.”
In other words, if the diet was rich in saturated fats, it would increased HDL, and if you replace the saturated fats with unsaturated fats (or synthetic trans fats), your HDL is likely to decrease.
In a 2010 meta-analysis of prospective cohort studies evaluating the association between saturated fat with cardiovascular disease, the authors, Siri-Tarino, Sun, Hu, and Ronald Krauss stated: “there is no significant evidence for concluding that dietary saturated fat is associated with an increased risk of CHD or CVD.”
In another article by the same authors: “An independent association of saturated fat intake with CVD risk has not been consistently shown in prospective epidemiologic studies, although some have provided evidence of an increased risk in young individuals and in women. Replacement of saturated fat by polyunsaturated or monounsaturated fat lowers both LDL and HDL cholesterol.”
Another study from 2010 (Yamagishi et al.) entitled “Dietary intake of saturated fatty acids and mortality from cardiovascular disease in Japanese,“ found that people who ate the most sturated fat had a lower risk of cardiovascular disease and the authors stated, keeping in mind that stroke is a bigger public health threat than heart disease in Japan: “SFA intake was inversely associated with mortality from total stroke, including intraparenchymal hemorrhage and ischemic stroke subtypes, in this Japanese cohort.”But can the associative studies be reconciled with experimentation and mechanisms of action? 
The Siri-Tarino (2010) article continued: “replacement of saturated fat by polyunsaturated or monounsaturated fat lowers both LDL and HDL cholesterol. However, replacement with a higher carbohydrate intake, particularly refined carbohydrate, can exacerbate the atherogenic dyslipidemia associated with insulin resistance and obesity that includes increased triglycerides, small LDL particles, and reduced HDL cholesterol. In summary, although substitution of dietary polyunsaturated fat for saturated fat has been shown to lower CVD risk, there are few epidemiologic or clinical trial data to support a benefit of replacing saturated fat with carbohydrate. Furthermore, particularly given the differential effects of dietary saturated fats and carbohydrates on concentrations of larger and smaller LDL particles, respectively, dietary efforts to improve the increasing burden of CVD risk associated with atherogenic dyslipidemia should primarily emphasize the limitation of refined carbohydrate intakes and a reduction in excess adiposity.”
In other words, it’s the carbohydrates, not the dietary fats that are contributing to CVD risk associated with atherogenic lipid dysreguation.
After we eat a meal with a lot of sugar and/or carbohydrates, the bloodstream gets flooded with glucose, and the liver takes some of the glucose and converts it into triglycerides for storage. The triglycerides are fused to the apo B protein and to the cholesterol that forms.
Gary Taubes wrote in Good Calories, Bad Calories (2007):
The triglycerides constitute the cargo that the lipo-proteins drop off at tissues throughout the body. The combination of cholesterol and apo B is the delivery vehicle. The resulting lipoprotein has a very low density, and so is a VLDL particle, because the triglycerides are lighter than either the cholesterol or the apo B. (In the same way, the more air in the hold of a ship, the less dense the ship and the higher it floats in the water.) For this reason, the larger the initial oil droplet, the more triglycerides packaged in the lipoprotein, the lower its density.
The liver then secretes this triglyceride-rich VLDL into the blood, and the VLDL sets about delivering its cargo of triglycerides around the body. Throughout the process, known poetically as the delipidation cascade, the lipoprotein gets progressively smaller and denser until it ends its life as a low-density lipoprotein—LDL. One result is that any factor that enhances the synthesis of VLDL will subsequently increase the number of LDL particles as well. As long as sufficient triglycerides remain in the lipoprotein to be deposited in the tissues, this evolution to progressively smaller and denser LDL continues. It’s this journey from VLDL to LDL that explains why most men who have high LDL cholesterol will also have elevated VLDL triglycerides. “It’s the overproduction of VLDL and apo B that is the most common cause of high LDL in our society,” says Ernst Schaefer, director of the lipid-metabolism laboratory at the Jean Mayer USDA Human Nutrition Research Center on Aging at Tufts University. None of this, so far, is controversial; the details are described in recent editions of biochemistry textbooks.
How this process is regulated is less well established. In Krauss’s model, based on his own research and that of the Scottish lipid-metabolism researcher Chris Packard and others, the rate at which triglycerides accumulate in the liver controls the size of the oil droplet loaded onto the lipoprotein, and which of two pathways the lipoprotein then follows. If triglycerides are hard to come by, as would be the case with diets low in either calories or carbohydrates, then the oil droplets packaged with apo B and cholesterol will be small ones. The ensuing lipoproteins secreted by the liver will be of a subspecies known as intermediate-density lipoproteins—which are less dense than LDL but denser than VLDL—and these will end their lives as relatively large, fluffy LDL. The resulting risk of heart disease will be relatively low, because the liver had few triglycerides to dispose of initially.
If the liver has to dispose of copious triglycerides, then the oil droplets are large, and the resulting lipoproteins put into the circulation will be triglyceride-rich and very low-density. These then progressively give up their triglycerides, eventually ending up, after a particularly extended life in the circulation, as the atherogenic small, dense LDL. This triglyceride-rich scenario would take place whenever carbohydrates are consumed in abundance. “I am now convinced it is the carbohydrate inducing this atherogenic [profile] in a reasonable percentage of the population,” says Krauss. “. . . we see a quite striking benefit of carbohydrate restriction.”