The saying "Men shouldn't keep cats and women shouldn't keep dogs" is a folk belief that suggests men are unsuitable for keeping cats and women are unsuitable for keeping dogs. This saying has no scientific basis and is therefore incorrect.
In modern society, choosing what pet to keep is a personal freedom and choice, and should not be restricted by gender, personality, or other factors. Both men and women can decide whether to keep a cat or a dog based on their own preferences and needs.

Of course, in real life, some families cannot keep both cats and dogs for various reasons, but this does not mean that the statement is wrong. Different people have different lifestyles and habits; some people may prefer cats or dogs, while others are more suited to other types of pets. The important thing is to respect everyone's individuality and differences, and not to easily label or make arbitrary judgments about someone.