A puppy is a ball of energy with fur, and all that energy needs an outlet. Otherwise, you run the risk that your puppy might be undersocialized. Compare that to a mature dog, who is already familiar with human contact and is usually content to spend his or her downtime kicking back, patrolling the house or snoozing. Of course, all dogs need playtime and attention. But an adult dog's needs are so much less.
Adult dogs are also better for families with young children.
A gentle adult dog will be more tolerant of kids and better able to seek out a safe place if he needs a break from the attentions of toddlers. Ditto for families with a dog already in residence. Often, they get a puppy, thinking it will be an easier introduction . But the high energy of a puppy can be irritating to an adult dog, especially a mature one. It's easier to add an adult dog who has been socialized with other dogs.