No, that's OK. The name of the game when it comes to gaining or losing body fat is insulin. You want less of it. Carbs are the only food you can eat to raise it substantially (protein does too, but much much less + you have to eat it anyway, so don't worry). That's pretty much it.
As for why you're eating fat while wanting to burn fat, it's just because there's nothing else to fucking eat. And it helps condition your body to burning fat (producing ketones, i.e ketogenesis) anyway. If you wanted to eat only protein, that would be called a PSMF, and you can do it, but it's honestly kinda dumb, and way harder than just not eating anything.
As an example take bacon and eggs. No carbs in sight, but plenty of fat. Try to think how shit that would taste if you took all the fat out and left just the protein, though.