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Pros
Pro They are small and can sit on your lap
...Or desk, while they do homework. Just make sure to supply them a square box or paper to lay on.
Pro Easy to take care of
Food, a litter box and a few shots every few years and a cat will tend to take care of itself. This is good for a kid that may not be able to handle the responsibility of a dog (which will require more attention). There is no need to take them outside, or really wash them all that much either. A hands off animal for the most part.
Pro Food is often cheaper
Food for cats generally costs less and they eat less of it compared to a dog. So when it comes to financial concerns they generally cost less over the years, illness withstanding.
Cons
Con Sharp claws
It may be easy for a child to get scratched from a cat that is not declawed (which most vets recommend not to do as it literally is cutting off their fingertips at the bone), which may also cause infection due to them digging in a litterbox when they go to the bathroom.
Con Usually do not get along with other pets or even other cats
Con Usually not very sociable creatures
They tend to keep to themselves.
Con Requires you to maintain a litterbox
Unlike a dog which you can just let out in the backyard. That is, if you have one.
Con Often coughs up hairballs
Sometimes requiring special medication or food.