that your nutritionist recommended you eat less saturated fat as a weight loss thing, which is wrong

One can also cut on fats to lose weight, if one doesn't proceed to eat more carbs and over-compensate in the end.

Normally, when someone is having trouble losing weight, they don't realise how many calories they consume, and errors with fat are the largest in terms of calories. When volition or judgement are impaired, that's when things get very messy and cutting down on fat may or may not result in eating more.