If your cat or dog has dandruff, is it just a bad hair day? Probably not.The three most common reasons for pet dandruff are allergies, parasites and inadequate nutrition. Pets need a proper balance of fats, proteins and other nutrients to keep their skin and fur healthy. Dandruff can be a warning of many health problems, so if you notice your pooch or kitty is getting flaky, get them to the vet for a physical.