Keep doing your research. Research entails looking at the issue from all angles, in this case, not just from the anti-purebred view.
First, look up the definition of purebred. It does not say that a purebred dog was never mixed.
In case you can't be bothered, here is the definition of "purebred"
(Life Sciences & Allied Applications / Breeds) denoting a pure strain obtained through many generations of controlled breeding for desirable traits
http://www.thefreedictionary.com/purebred
Dogs that were once mixed were selectively bred over many generations for desired traits with a specific goal in mind. They eventually "breed true", that is consistantly produce a those traits without having to go back to the original breeds. When you breed a German Shepherd (one of those breeds that were once mixed, actually with more than one different type) to a German Shepherd, you get a known set of characteristics that will appear. THAT is a purebred, not a dog that was never mixed.
Not to mention these breeds were mixed to produce a dog with specific traits for a specific purpose. They were not randomly created breeds to make money, they had a purpose, usually a working one. What is the function of a Labradoodle? it was intended to be a hypoallergenic service dog, but that was not successful.
With these "designer dogs" you do not have a reliable set of characteristics that appear. They are mixed breeds and do not breed true. Many of these breeders will not breed past the first or second generations, meaning they will never breed true.
Check out the variations in only coats in Labradoodles here
http://www.acmecreekkennels.com/Acme%20Creek%20Labradoodles/labradoodle_coat_types.htm
That is not even mentioning any other trait, like size, temperment, drive, color, etc.
Check out the variations in looks, size, etc
http://www.acmecreekkennels.com/Acme%20Creek%20Labradoodles/labradoodle_gallery.htm
Now go look up any recognized breed, here are some German Shepherds and see the difference.
http://www.pedigreedatabase.com/gsd/pedigree/565016.html
And no one here hates mixed dogs (well maybe one person). I, like so many others love all dogs. Many here own mixed dogs. What we hate is breeding intentionally, calling it a cutsey name and charging a fortune when the same mix is dying in a shelter.
Add- just for reference, GSDs are a relatively new breed, which came about in the early 1900s.
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Being a purebred and being recognized by the AKC are two completely different things. There are many breeds that are true breeding, ie purebred, that are not recognized by the AKC, some are recognized by other reputable registries.
AKC is not the supreme being.