Myth: Eating Fatty Food Makes You Fat
Truth: Eating fatty foods does not make you fat. Fat in moderation is a necessary part of any healthy and balanced diet. Putting on more weight in the form of fat is a result of energy imbalance. You will gain weight if you take in more calories than you burn. Fat is a concentrated source of calories, but it is not necessary to eliminate fat from your diet completely.
Whole-food fats (nuts, seeds, avocado) are satiating and help you feel fuller for a longer period of time. You can't put French fries and almonds in the same category simply because both are "high in fat." Foods like French fries don't fill you up. They also don't contain other useful nutrients like foods with good fats (as per mentioned above).
Fat can make you fat, but so can carbohydrates and protein. Basically, the overconsumption of any food group has the potential to increase your fat and overall weight. Granted some fats are seen as 'better' than others (such as coconut oil and fish oil relative to trans fats) which accounts for some variability in weight gain, but weight gain will occur when 'excess' is consumed (whatever that may be to your body).
In summary, fat won't make you fat, unless you eat too much of it. You have to beware of fat free, as well, as it often actually contains fat and adds quite a bit of sugar. When something gets eliminated, make sure to find out what filled the void.