Not all fat people can lose weight easily.
Many have hormonal problems. These can be intrinsic hormonal problems, or they can be exogeneous. If your doctor puts you on insulin or prednisone, you're guaranteed to put on body fat even if you cut calories and do more exercise, that's been proven.
Further, a lot of the advice on losing weight -- do cardio and eat less -- is wrong. The strategy of "eat less, do more cardio" has a 93% failure rate so it doesn't work, but that's what people are told to do to lose weight. The effect is even worse when people follow low-fat diets that are also low in cholesterol, as recommended by most doctors.
This was shown in the 1940s Minnesota Starvation Experiments. If you just cut calories to 1600/day on a standard diet, metabolism crashes in most people, they feel like they're freezing, they're irritable, and they start hurting themselves, it doesn't work. They end up weighing more than when they started.
A 1980s study from Denmark took sedentary adults and trained them to run a marathon. You know how much weight they lost from cardio? The average among women in the study was 0 lbs (yes, 0 lbs), and the average among men was 5 lbs. Moderate intensity continuous cardio, e.g. jogging for 60-90 minutes, is simply not a good strategy for cutting fat. That's known from measurements. The body compensates by either decreasing metabolism, or increasing appetite.