It is not really a mystery any more. There was a heart disease epidemic in the mid 20th century (the rate doubling every decade). A scientist named Ansel Keys did an epidemiological study comparing rates of heart disease to fat intake in 6 different countries and found a strong correlation: countries that ate more fat had higher rates of heart disease. Therefore fat causes heart disease.
This is the lipid hypothesis, which still drives nutrition advice and laws today.
Ansal Keys joined the board of The American Heart Association which adopted the lipid hypothesis and started telling everyone to cut out fat and eat more carbohydrates (carbs are sugars strung together which are quickly chopped up and metabolised as sugar, what could go wrong? ;). Numerous clinical trials, involving tens of thousands of people, all failed to find a link between fat and heart disease (often actually finding the opposite). The government ignored these trials and supported Ansal Keys instead.
The Mcgovern senate committee was tasked with creating a national nutritional policy in 1977, but when scientists told the commission that there was no evidence supporting the low fat/high carb diet and that more research was needed to confirm the hypothesis, they where told that the government does not have the luxury of waiting for scientific research [0] and in 1980 the USDA published the dietary pyramid that we still use today, recommending that people get the bulk of their calories from carbs.
The single epidemiological study by Keys was all they had to go on at that time. Since then, there have been many more rigorous diet trials which failed to confirm the lipid hypothesis and actually show a strong link between carb consumption and obesity. So the scientists introduced an entirely new scientific method, now called teleoanalysis[1][2] to prop up the lipid hypothesis. No causative link between dietary fat and heart disease could be found in controlled trials. But, they did find an association between fat and cholesterol, and then they found an association between high cholesterol and heart disease. So now using teleonalysis we can say that fat is associated with high cholesterol and high cholesterol is associated with heart disease therefore fat causes heart disease.
The American government officially supports the lipid hypothesis and promotes the high carb diet pyramid at all contact points. Schools, universities, government agencies all must promote the lipid hypothesis or be sacked or defunded; "The dietary dogma was a money-maker for segments of the food industry, a fund raiser for the Heart Association and busy work for thousands of fat chemists... To be a dissenter is to be unfunded because the peer-review system rewards conformity and excludes criticism"[3]
Carbs have low nutritional content and most vitamins are fat soluble so by eating less fat you feel more hungry because your body needs those nutrients and you are forced to eat more. When you eat a lot of carbs, your liver gives you an insulin shot. Insulin tells your fat cells to absorb the carbs to bring the body back to balance. So your fat cells swell and then divide, making your body bigger, and a bigger body requires more food to sustain it.
The result is that obesity and heart disease have increased about 10x since 1980 [4]
[0] https://www.youtube.com/watch?v=xbFQc2kxm9c
[1] https://www.bmj.com/rapid-response/2011/10/30/teleoanalysis-...
[2] https://stats.stackexchange.com/questions/65372/what-is-wron...
[3] https://books.google.co.uk/books?id=CxKQ2Ak6_p4C&pg=PA144&lp...
[4] https://www.ahajournals.org/cms/asset/d4e7b1a9-3093-4507-984...
