Every situation is different, and every animal is different so we can never be 100% sure if a cat and a dog will get along. Each animal has their own personality and their response to other animals can vary.
Take our house cat Archie. I chose Archie because of his large size and big jaws. The shelter needed a chief mouser and he fit the bill well. He gets along with people of all ages. But watch out if he sees a dog! I have witnessed him getting out of his bed, charging across the counter, and swiping at newly arrived dogs. On the occasion that I have my dog with me at work, he has crouched down as if to pounce but once I get between him and my dog, he stays put. Archie does like to sleep in my office though and the first time I had my dog with me, Archie did avoid his comfy bed for most of the day. By the afternoon he must have decided to chance it. He jumped on my desk (which he does frequently) and I started to pet him. He dodged my attempts to pet him so I stopped. He then looked under my desk to check out my dog. After assessing him for a few seconds, he must have decided that he wasn't a threat. Maybe it is because Archie is as big, if not bigger, than my dog. Whew, crisis averted.
Adopters have sent us lovely pictures of cats and dogs curled up together so I know it is possible to have peace in the household. My cat at home avoids the dogs because one of the dogs wants to rough house with him.
Sometimes we know that dogs will not do well with cats; as in they might eat them. It may be because of their breed, hunting instincts, and/or prey drive. We can pass that information on to potential adopters to avoid catastrophe.
But if you like both cats and dogs, I can tell you , it is possible for the right animals to live together in the same household.