That's not at all how natural selection works. Successful traits are passed on and unsuccessful ones aren't. In the case of dogs, the canids able to tolerate being around prehistoric people were able to eat the scraps and early man found the canid provided protection and warning of other predators, it was very much a symbiotic relationship.

Feline and man for all intents and purposes just kind of agreed to exist together. As we developed agriculture and formed permanent settlements the grain attracted rodents which in turn attracted cats. The cats provided free pest control and companionship and are self-cleaning so were essentially given free reign, that relationship remains relatively unchanged.