Animal fat, you know, the white spots. Is it healthy to eat with the rest of the meat or should it be avoided?
Eating less saturated fat (mainly present in animal fat) should be healthy, although the calories you miss by not eating saturated fat shouldn't be replaced with carbohydrates (most other food in the American diet). It lowers your odds to get cardiovascular diseases, you won't live longer on average.
You might be better off not eating the whole peice of meat. Recently the WHO also put red meat on the 2A list of carcinogenic compounds, saying that red meat consumption probably increases your risk of colorectal cancer. The risk is not that high though. For processed meat (sausages, bacon) they're more sure.
However, if you look at it from the point of view of an average obese American, you might be better off eating the fat and meat, and just not drinking your coke, as obesity is a major cause of morbidity. It has been shown that low carb diets work better than low fat diets.