There are a number of issues going on here. First, you might not be getting enough protein. Protein is a primary need, and if the protein-leveraging hypothesis (first propounded by Raubenheimer and Simpson) is correct, we will not be satisfied by any number of calories until our protein need is met.
Second, some people find fat relatively more satisfying to their hunger than protein, while others find they need relatively more protein and a bit less fat. You might consider ditching your rule for the proportion of what to eat and just consider eating to satisfy your hunger.
Third, when people recommend 2:1 fat to protein, they are generally talking about the ratio in terms of calories. This is pretty easy to achieve, since an equal amount of fat and protein by weight is 69% fat and 31% protein by caloric value. Remember that a gram of fat contains more or less 9 calories, while a gram of protein contains more or less 4 (and remember that even the “precise” numbers are still averages, not to mention that we when we talk about food the “calories” we are speaking of are what physicists call kilocalories).
Fourth, while we need protein daily, and are programmed to instinctively get pretty much the right amount each day, the body does not generally use protein as fuel, generally preferring it for structural purposes (muscles are pretty much all proteins, and even bone is calcium in a protein matrix). Because of the lower ATP yield from proteolysis, the body prefers to metabolise glucose (glycolysis, which is a fairly fast reaction with a decent ATP yield) or fat (fatty acid metabolism, which is slower, but which yields the most ATP). The body will, however, metabolise protein (muscles, organs, etc.) during starvation, in order to preserve its fat store for later in the process.
Fifth, the best fat for energy is monunsaturated. Since butter is about 51% monounsaturated fat (plus about 47-48% saturated fat, and the rest various polyunsaturates), that may be why the butter satisfied you. (A very high percentage of the walls of every cell in your body is either saturated fat or cholesterol, by the way.)
Sixth, despite all the propaganda put out by the American Heart Association in favour of “vegetable” oils (remember that the organisation was put on the map in the late 1940’s by a large donation from Crisco Oil and they have stayed loyal ever since), the best fats, even for heart health, are saturated and monounsaturated fatty acids. Saturated fat raises your HDL number much better than any drug on the market, and the monounsaturates are good for stable endurance energy. This is not to mention the fact that polyunsaturates, especially the ω-6 fatty acids, can cause systemic inflammation when consumed in quantity and most of the “vegetable” oils on the market (actually, they are seed oils) contain a startlingly high percentage of ω-6 fatty acids. This is why we recommend cooking with butter/ghee, tallow, lard, and bacon grease, and making your mayonnaise and salad dressing with one of the fruit oils (avocado, coconut, or olive).