"The cat tries to get away, the dog thinks the cat is inviting it to a game, and so chase ensues with neither party understanding what the motivation of the other one is," says John Bradshaw, an anthrozoologist and author of myriad books about cats and dogs.
Looking at the miscue from an evolutionary standpoint, Bradshaw would remind us that dogs are descended from the highly social wolf. On the other paw, domesticated cats descend from the mostly solitary Arabian wildcat. In other words, you can't really blame either species for the kerfuffle. Each animal is just practicing behaviors that have been proven to help it survive through the eons.
"Compared to their wild ancestors, cats are actually remarkably good at getting on with other cats and people," says Bradshaw, "but it's clearly a process that's not gone as far perhaps as we'd like it to go." (Indeed.)