Like ebola said, the amount of genetic variation between different groups of people is extremely small. For example, there are chimpanzees in the same tribe who have more genetic differences than exists between, say, a generic African and a generic Native American.
What's more, breeds of dogs are an especially bad comparison since they have been created specifically for various traits. Humans, by contrast, have separated mostly by random drift, with only a few traits being selected for -- skin color and body fat, for example.
And finally, dog breeds actually exist. Registration and selective breeding has led a selection of well-defined breeds, as well as just the run of mutts. Human beings are all mutts. There's no such thing as a well-defined human "race." There is genetic variation among human populations, yes. But any attempt to divide people up into distinct "races" is just a matter of artificially drawing boundaries. There's really just gradual variations between populations in all sorts of various ways. People generally decide how many (and what kinds) of "races" they want based on cultural/social factors, and then shoehorn in people into those categories.
You can certainly compare dog breeds to human "races." (I just did!) It's just not a very good comparison. Sort of like comparing, say, Tony Blair to Hitler. You can find points of similarity, but they're really not alike.
