Step 1: Use a simple physical clue, not just chemistry rules.
Think about butter or ghee sitting on a kitchen shelf, they stay solid at room temperature, while cooking oils stay liquid. This physical difference is a direct clue to their molecular structure.
Step 2: Connect solid or liquid state to saturation.
Saturated fatty acid chains are straight and pack tightly together like neatly stacked pencils, which raises the melting point and keeps animal fat solid. Unsaturated chains have kinks from double bonds and cannot pack as closely, which is why vegetable oils stay liquid.
Step 3: Check statement A against this reasoning.
Since animal fats are solid, they must be mostly saturated, not unsaturated as claimed, so statement A is the false one.
Step 4: Quickly confirm the other three are sound.
Unsaturated oils being healthier for cooking is correct, vegetable oil decolourising bromine water because of its double bonds is correct, and hydrogenation of oils using a nickel catalyst to make solid fats is also correct, so nothing else is wrong. \[ \boxed{\text{Animal fats generally contain unsaturated fatty acids}} \]