Why do cats keep crying to be let out and then cry to be let in again?

Cats hate doors. Doors simply do not register in the evolutionary story of the cat family. They constantly block patrolling activities and prevent cats from exploring their home range and then returning to their central, secure base at will. Humans often do not understand that a cat needs to make only a brief survey of its territory before returning with all the necessary information about the activities of other cats in the vicinity. It likes to make these tours of inspection at frequent intervals, but does not want to stay outside for very long, unless there has been some special and unexpected change in the condition of the local feline population.

The result of this is an apparent perversity on the part of pet cats.

When they are in they want to go out, and when they are out they want to come in. If their owner does not have a small cat-flap on the back door of the house, there will be a regular demand for attention, to assist the cat in its rhythmic territorial supervision. Part of the reason why this repeated checking of the outside world is so important is because of the time-clock message system of the scent-marks. Each time a cat rubs against a landmark in its territory or sprays urine on it, it leaves a personal scent which immediately starts to lose its power. This decline is at a steady rate and can be used by cats to determine how long it has been since the scent-marker rubbed or sprayed. The repeated visits by a cat to inspect its territory are motivated by a need to reactivate its fading scent signals. Once this has been done, comfort and security beckons again, and the anxious feline face appears for the umpteenth time at the window.