A few random comments on this subject…...
To me, a mutt is a dog comprised of multiple breeds and of unknown ancestry. I prefer the term "crossbred" or "crossbreed" in reference to a dog with purebred parents of two different breeds. I do not use the term "hybrid". I was always taught that a hybrid is a cross between two animals of the genus but different species. For instance, a cross between a male donkey (Equus asinus) and a female horse (Equuus caballus) creates the hybrid mule. A cross between a male lion (Felidae leo) and a female tiger (Felidae tigris) creates the hybrid liger. But a cross between a Pug (Canis lupus familiaris) and a Beagle (Canis lupus familiaris) just creates more Canis lupus familiaris aka domestic dogs.
So what is the appeal of "designer dogs"? Quite frankly I believe it has alot to do with the media. TV shows of all kinds have featured segments on "deisgner dogs", almost always portraying them as being healthier than purebreds and possessing the best traits of each purebred parent. Even with zero evidence to support these claims, the public bought it hook, line, and sinker and the demand for crossbreds escalated at a rapid pace. Almost overnight, it seemed like everyone had to have a Labradoodle or a Puggle. "Breeders" everywhere with dollar signs in their eyes started cranking out puppies by the hundreds (thousands?) and there were no shortage of buyers.
My personal feelings are that crossbreeds and mutts can make delightful family companions and there are people who cherish these dogs. When people make derogatory comments to the owners of these dogs, to them it is like a slap in the face. No, I don't "approve" of "breeders" who toss a couple of dogs together, be they the same breed or not, with zero concerns about health and temperament. I'm just saying that if a person already has a dog from a less than desirable background, we should be aware of their feelings.
Ok that said, and I know this comment may get me "flamed", there are a handful of breeders who cross breeds who I would consider to be responsible breeders. They do generations of health testing, provide very good warranties/contracts, carefully screen homes, and provide long-term support for their buyers. If a person has their heart set on a Cock-a-poo or a Labradoodle puppy, there are places to get one that is properly produced.