As many as three in 10 people in the U.S. have allergies to cats and dogs, and cat allergies are twice as likely as dog allergies. Allergies happen when someone’s immune system is triggered by something, such as pollen from flowers, or dander from pets. These allergies can cause itchy watery eyes, a runny nose, sneezing and rashes just to name a few, and it can make owning a pet extremely uncomfortable.