I don't think it's that they are annoyed at the breed itself, my last service dog was a rescue, golden / Labrador, 2 different breeds accidentally bred and surrendered. She was a super smart and super calm dog that loved being with people. My first service dog, beagle, shepherd, springer and something colorful, our best guess. Again they found her at the humane society, her breed was mis sakes but they thought she was cute and tried training her, she passed all the puppy tests and she was super social with all snimsls. So I have no problem working with mixed animals, however many of the designer animals are just that,mother common sense or good personality has been bred out of them.
Take the Italian greyhound/pug cross or the chihuahua /Great Dane - the idea of that was to breed a mini Dane but that's not how it's done. You had asked why people are annoyed at cross breeds especially ones that don't work? If I were to get a herding animal say I want to chase Pygmy goats in to the barn, I buy a dog, train it, spend hundreds of hours teaching it all it needs to work and let it out with the goats. The dog either chases after the goats and bites them rather than just nipping and barking to get them going, such as they crossed the boarder collie with a bulldog, one is bread for taking care of stock and their welfare, the other eas bred for baiting bulls and helping taking them down for the owners. Put both breeds in one body, can you tell which instinct the pup will get? Imagine 2 pups from the same litter both look identical however the first pup is stubborn, slow to learn and bites the livestock to the point it draws blood, it's half boarder collie so why is it so aggressive? Take the second pup have it do the same trial, it's in with the livestock and watchful over it, can move them as directed and no problems so what's the problem? We will pretend that I know nothing about dogs so I take dog number 1 out in the cattle pen to help get a rogue dos out of the group, the dogs duty is to keep all the other cattle away from me and the dog does an excellent job nipping and chasing them away. Dog 2 from same litter takes over in the afternoon, and not only does the dog not work the cattle, it refuses to protect me by. Upping at the cattle and gets itself kicked and me endangered by its running away. With a mix you don't know which parents gene pool is going to come through even though it's the same litter.
With all the mixed puppies we have seen born by the time they are 8 to 12 weeks old some pups can be very friendly and outgoing, they can have long wavy hair and are long legged gangly pups, the other half of the litter are short squat dogs, stubby legs, short tails, short hair, but they both had the same mom and dad so what happened? What will pass to the next generation and to the next?
Cocapoos were all the rage in the 60's and 70's. Conversation was like - hey do you have a cockapoo? Today is, Do you have a Labradoodle yet?
There is nothing wrong with mixed breeds other then you cannot depend on which parents traits the pups will get, making more and more pet quality puppies to the point more are being euthanized daily then are being born currently. Dogs that are accidentally bred a one thing, but to bread your dog back to back to back for the whole 9 years the dog is breeds le isn't fair to the dog, breeding the same dog to s different dog breed to see ehst comes out the cutest and makes the most amount of money sent right either. Breeding for a good temperament, sound body - eyes, hips, elbows etc no degenerative diseases, No bad backs,,hips,,shoulders, no missing teeth or undershot or overshot, blind and or deaf dogs. Yet people breeding the designer dogs have not been paying attention to how healthy the pup is and how they can improve on the "new breed they invented" when the pups come out and they are fragile, get sick at the slightest whatever, break bones too easily, such as when they are just running, and worst yet have such high risk of organ failure, cancer and other more rare diseases seem to affect the designer breeds more then the standard dog, I'm not saying purebred are healthier, but w good solid dog from s good solid bloodline that has been hip, elbow, etc certified is less likely to pass on bad hips etc to its offspring, and the good breeders spend their money to get these dogs tested, not just "hey let the dogs out and see who takes her first!" Style of breeding.