TABOO RELATIONSHIP

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By nature, dogs are predators and often chase things smaller than them—including cats. However, this doesn’t mean that dogs and cats are not able to live in harmony. As the two most common household pets, the way dogs and cats relate to each other have a lot to do with their temperament, and whether either have had any adverse reactions to members of different species in the past.
For example, a dog raising his paw to a cat may mean he wants to play, but a cat can take it as a sign of an attack, prompting the cat to swat her paw at the dog, sending her into a hissing fit. Likewise, a cat that tries to rub up against a dog may be acting friendly, but a dog can interpret that as a threat—especially if the cat is near his toys or food—and can cause the dog to growl or bark.

However, getting a puppy and a kitten at the same time and raising them together is an option: that way neither has previous fears of each other, unless one of the animals is overly-aggressive and domineering.