How to Prevent a Cat From Getting Out a Doggie Door

Get an electronic pet door. These are doors that require wearing a collar. When Fido approaches the door, the collar emits a signal that unlocks the door long enough for him to get out. As long as you don't give Fluffy a collar too, he'll be stuck inside the house.

Switch to a doggie door made with heavier material than just a soft plastic. Cats will push through a plastic flap easily, but they might not like pushing through a heavier door in order to get through. Some doggie doors come with strong springs that a cat should not be able to push through -- unless you have a supercat, which is always a possibility. Or you can use some Velcro or double-sided tape to secure the flap, so it requires more of an effort to get it open. All but the smallest dogs should have no problem, but the cat might give up if it's too much work.

Close off the room that has the doggie door. Can you keep the cat away from the kitchen or the room where the door is? You can keep the doggie door locked most of the time, and then unlock it for a couple of hours in the morning and afternoon. During those times, keep Kitty somewhere else.

Get ready with a squirt gun. This is probably not the most practical of methods, since it requires you to sit near the doggie door and squirt the cat every time he tries to get out. The idea is that eventually Kitty will learn that getting near the doggie door means getting wet, and he'll decide not to try anymore. If you have a stubborn cat, the learning process might take a long time.