I see people on here saying to speed the weight loss add fat and weight lift.
Then someone asked how to gain weight and several answered add fat and weight lift.
How can fat be key to both losing and gaining weight?
I think it depends on the amount. When I see people who are trying to reduce being told to eat more fat, their intake is usually very low in fat. They're eating lean meats and only adding a smidge of oil here and there. They're cutting out the carbs and non-primal foods but they're still cooking like fat-phobic CW taught them to. That's not going to give them enough fat to thrive and they're going to be miserably hungry. Now if you eat too much and have a surfeit of calories, then you're in weight gain territory.
Lifting heaving things is the key to gaining muscles (muscle weight) so you'll hear that every time someone say they want to "gain weight".
Fat and carbs can both be burned by one's body as fuel. So, if you've eliminated most of your carbs you will need to eat fat for you body to burn so that you can lift the weights that you will need to build muscle. It's also a good idea to carb cycle because fat does not replenish the glycogen supply in your body and eating a limited amount of carbs will give you the ability to store some glycogen without gaining much fat.
If you are not eating enough fat or carbs you will be running on a caloric deficit and and depleting your body's fat reserves. If, however, that deficit is too extreme then you will find yourself running short of energy and unable to do things like lift heavy objects so that your muscles will get larger over time. Therefore you might need to eat more fat. Somewhere in the middle is a delicate point where the balance point between losing fat and gaining muscles. It's the holy grail of the fitness world.
So, if you want to gain muscle mass then lift heaving things and eat enough protein to build your muscles and in order to vary the amount of fat that you have stored eat more or less fat and carbs. They're really two separate processes.
Also, when trying to gain weight, it's often actually difficult to consume enough calories, and fat is the most calorically dense macronutrient.