Preheat the oven to 350 degrees F (175 degrees C). Spray a 4x8-inch loaf pan with cooking spray.
Beat egg whites in a glass, metal, or ceramic bowl until foamy. Gradually add cream of tartar, continuing to beat until soft peaks form. Set aside.
Combine coconut flour, almond flour, arrowroot powder, baking powder, and salt in a bowl and mix well.
Beat egg yolks using an electric mixer in a bowl until thick. Add coconut oil and honey; mix well. Add flour mixture and stir until well combined. Fold in 1/4 of the beaten egg whites until incorporated. Add 1/2 the remaining egg whites and gently fold until only small amounts of egg whites is visible. Repeat with remaining egg whites. Pour mixture into prepared loaf pan and smooth the top.
Bake in the preheated oven until nicely golden brown on top, about 35 minutes. Remove from oven, set on a wire rack, and let cool for 10 minutes. Run a knife around the sides, tip out bread onto a rack, and let cool completely.
13.7 g fat; 9.8 g carbohydrates; 6.3 g protein