Why does my cat constantly ask to be let outside?

Cats that are not spayed (intact females) are particularly likely to do this behaviour when they are in heat. If a cat is spayed, the surgery may result in elimination of the behaviour by removing the source of the female hormones that trigger the male seeking behaviour.

In the case of spayed female cats, it could be that as a younger cat she was used to being outside. Providing lots of attention and toys/playtime during her waking hours may help to keep her interested in the household environment. If she is busy when awake, she is less likely to yearn for action outside the home.

Sometimes outdoor cats come around and call, and this can also trigger this type of behaviour in an indoor cat. This is obviously very difficult to control since it involves a free ranging neighbourhood cat.