Really, it's why buy from a responsible breeder? There are people out there who breed purebred cats (or dogs) simply to make money selling the offspring. Those are not the people I'm talking about, and responsible breeders go to great lengths to keep animals out of the hands of those people. I'm talking about people who breed because they love the characteristics of a particular breed of dog or cat (goat, whatever) and want to preserve and improve those characteristics. These people care very much about the health of the animals they bring into the world. They do whatever genetic testing is available, and they provide a home if an animal they bred needs it. They give guidance and education to people who buy a kitten or puppy from them. The real question is, why would you not buy a pet from such a person?
Now, I'm not against "rescuing" an animal in need and giving it a home. I'm just saying people should realize that all choices of where to buy an animal have an influence on the supply chain. And yes, you are buying a pet, wherever you get it. The price may be "free" or very low from your next door neighbor or the animal shelter, but you are making a purchase decision. Hopefully, you are also "adopting" a pet that will be a member of your family for life. Any cat costs about the same to keep, where ever it comes from.
Let's consider some of the options. I'll probably use dogs mostly as examples but I'm referring to cats also. One choice is the local humane society. The advantage here is that your purchase price will be low and you are giving a home to animal who may otherwise be in danger of euthanasia. Many people like the idea of saving an animal. The downside is that you roll the dice on what you get. Some people think "mixed breeds" are healthier than purebreds, but this is not really true. Mixed breeds carry all the same potential health issues as purebreds and no one has screened to try to reduce the likelihood of genetic problems. You also have no idea what the likely personality of a kitten or puppy will be, or possibly even the adult size. Adopting an adult can help solve this, but many people want a puppy or kitten. I think most shelter kitties turn out fine. There is a lot less variability in cats than in dogs. The biggest risk with a shelter cat is that it will have a health issue you will be stuck dealing with, but many shelter cats are healthy. We have a thirteen and a half year old domestic shorthair who has never had a health issue in her life. She has moved all over the country with us. So a humane society is not a bad choice if you're not too picky about having particular personality or appearance characteristics.
Suppose you do want something particular, a toy size dog or a longhair cat for example. Another option is a breed rescue group. Most of these pets are living in a foster home, waiting to be adopted. Typically, you will pay an "adoption fee" of a few hundred dollars to get an animal from one of these groups. Yes, they are covering expenses, and you are "buying"your pet. You may or may not pay less than you would from a reputable breeder. Prices tend to be tied to the age and health of the animal. Many of these groups deal with a particular breed of dog or cat, but some have multiple breeds. On the positive side, if you want to "save" an animal but you also want a purebred, this is a way to do so. On the down side, there is a reason some animals end up in rescue. They often tend to be older, you may have to wait a long time for a puppy or kitten of a particular breed. You may not, it varies. They may have health issues because they may come from situations where they have not been well-cared for. They often have emotional issues. Those rescued from "bulk breeders" don't know how to live in a home. Usually you can expect to need to do some training. Rescue dogs usually need house training. Expect to be taking on at least as much work as if you got a puppy or kitten that needs to learn to socialize and be a good member of society.
Something that doesn't get talked about is that much of the original source of breed rescue animals are puppy or kitten "mills". Adopting from a rescue group does provide a secondary market for these mills to continue producing. These mass producers don't care where the animals end up, and the animals are in need of homes, so you'll have to decide for yourself what you think of this conundrum. We do have a papillon from a papillon rescue group. He found us at an agility trial and let us know he was our dog! He has been very healthy, but I know he came originally from an Arkansas puppy mill. He is way oversized for a papillon (which makes him a great kids dog!) and his conformation leaves a lot to be desired. He came from a home where he was neglected, but not abused and his issues have not been too difficult. We have had to deal with marking in the house. Breed rescue is a good option for some people, just know what you are getting into.
What is wrong with buying from a reputable breeder? Nothing! If all hobby breeders quit breeding you know what would happen? Extinction. That is what happens when breeding populations get below a sustainable level. There are some very rare breeds actually facing this situation. If you happen like papillons, Australian shepherds, Maine Coons, or whatever you fancy, by all means support the survival of the best of that breed by buying from a good breeder. If only puppy mill and mixed breeds reproduce because everyone buys a rescue and spays and neuters the best quality animals then eventually only low quality animals will be available. Perhaps they won't be available at all, at least not at a price the average person can afford. Really, where should we want our pets to be produced from, the best stock, or the worst? Because here is another reality. As breeders have become stringent about placing pets on spay and neuter contracts and being very careful of placing intact animals, what do you think is the source of most rescue and humane society animals? It is not healthy, high quality breeding stock. It is what is left that indiscriminate breeders can get their hands on.
One of the biggest Maine Coon sites on the web is populated by a majority of cats that are not even Maine Coons. They are domestic longhairs. How do I know that all these rescue cats aren't "Maine Coon mixes"? Because Maine Coon breeders aren't losing track of their cats to be producing all these rescue mixes. People must want certain breeds. Sites like Petfinder.com are always listing dogs as being of a certain breed, even when the dog in question bears little resemblance to the breed named. Presumably a cat listed as a Maine Coon or Maine Coon mix is more likely to find a home than a plain domestic longhair. If you want one of these pets, you should certainly please yourself. If you prefer to know the background of your pet and want a particular model and performance, buy what you want, guilt free, knowing that you are supporting the perpetuation of the best of the breed you love.