Dogs are unable to breed with humans, in the sense of copulating to produce offspring, because humans and dogs are too different to produce viable embryos. A dog mating with a human in a non-reproductive capacity can cause injury and may infect the human with a zoonotic disease.
Dogs and humans, although both mammals, are not particularly closely related. Humans have 23 chromosomes in their reproductive cells, whereas dogs have 39, making combining the two cells to create a fertilized egg a very poor prospect at best.
Sex between humans and dogs is dangerous to both, as the sexual organs of either species may cause internal injuries to the other, the animal may bite or fight off the human attempting to copulate with it, and certain exotic diseases can cross the species barrier to infect the human and the dog. The illnesses one can catch from sex with a dog include roundworms, salmonella and life-threatening Brucellosis.