Sometimes called "Bullet Proof Coffee."
Our fear of fat runs deep.
The solution is just do it. Every time you remember.
Over time you'll come to understand that when you put butter in your coffee, you find that you drink coffee less often. You will also be less inclined to snack.
However I've still taken months to get into the habit of ALWAYS adding butter to my coffee.
I know that when I do that, the whole business about needing a snack again soon after a meal goes away.
The butter settles the craving for more food. So you don't need that snack.
Adding butter to your coffee has a purpose, to stop you snacking, and to give you energy.
If you are established in the diet, but not losing weight, perhaps not putting butter in your coffee is the right move. Especially so once the intermittent fasting routine is established.