I spent the last 20 years of my life "dieting" always low fat and whole grains... sure I lost weight, even lost 80lbs one, but it all came back. 20 years of doing the same thing expecting something different.
Like you I was very resistant to fats, but after some time of playing with Paleo (minus the high fats) and reading some success stories here I figured I'd bite the bullet and go with it.
At first it was kind of shocking to see the bacon grease on my plate or the olive oil in my salad, but I committed to give it a try. One thing I took to heart was that if I was going to eat high fat, then my carbs needed to be low, like it has been said already "excess calories in the presence of elevated insulin" is what helps us gain weight.
I went into it head first. 80% fats, 15% protein and 5% carbs from veggies and fruits. What I found was that I lost weight just the same as when I was doing low fat high carbs, but it was easier. I actually had to try and find ways to meet my daily minimum which was around 1200 to 1500. I would have breakfast at 5 am... and wouldn't feel hungry until around 11 am... 6 hours.
I will admit the first few weeks my tummy was making all sorts of noise, but once it became accustom to it, all was good.
I have since upped my carbs and lowered my fats and protein. But I still stay under or around 100g of carbs a day with one or two days going up to 150. It feels like this is the best for me, though others may eat more or less.
I no longer fear healthy fats. I now have a "fear" of canola oil, and other vegetable fats as well as "low fat" products. The other thing that made the switch easier was knowing that that low fat products usually have to compensate for the lack of flavor by adding sugar.
Cooking with healthy fats also tastes delicious once you get over the fear of fats. I can't go back.
edit to add: I also find that I can eat up to around 1600 calories a day and still lose weight. As long as my carbs are lower and from real foods.