Why is it important for living things that water and oil do not mix together?

For some living animals have oily feathers or coat to protect them from moisture. Water and oil doesn't mix because water has polar molecules while oil has non-polar molecules. Non-polar and polar molecules can't bond together. By this reasoning, since some animal's coat and/or feathers are oily, the oil repel the water and helps them stay dry and maintain their body heat which is necessary for survival.