Having a dog doesn't mean you can never get a cat or vice versa. It just means you need to prepare for the effort required in training one to accept the other.
It can be easy to understand the danger a dog might pose to a cat. Dogs are generally bigger, stronger, and have larger teeth. However, that doesn't mean that cats are defenseless. An angry cat could easily blind a dog with their claws or inflict a painful bite. For the sake of both animals (and you, if you have to break up that fight), it is best to introduce them to each other slowly and train them to accept the other as part of their environment. Keep in mind, however, that some cats just may not accept a dog and some dogs just cannot live with a cat. Have a back-up plan ready just in case you need to find a new home for one of the animals.
It is important that the introduction between the two animals happens gradually. When you bring the new animal home, seclude the old animal in a separate room or somewhere where it can't see the new animal. After letting the new animal explore for a short while, seclude it and release the old animal to allow it to smell the new scent. Repeat this process for several days until both animals have no reaction to the new smell of the other. Now that they are accustomed to the scents, it's time to start on the sight. Allow each animal to see the other, either from a crate or through a cracked door protected by a gate. Start off at just a very brief look and gradually increase the time. Remember to reward good behaviors, like not barking or howling, with special attention or a treat. After a few days when the animals are used to this level of interaction, start giving them more natural exposure under the control of leashes. After several interactions with no negative reaction, you should be ready to supervise the animals as they freely interact with each other. Make sure you supervise them at all times and the cat has a chance to escape if it needs to.
With some animals, you may never want to have them alone together when you leave without confining them to separate rooms. With some time and patience, you can enjoy the best of both worlds.